MAT540 Week 2 Quiz 1 Latest 2017 March Question 1 2 out of 2 points Probabilistic techniques assume that no uncertainty exists in model parameters. Question 2 2 out of 2 points In general, an increase in price increases the break even point if all costs are held constant. Question 3 2 out of 2 points If variable costs increase, but price and fixed costs are held constant, the break even point will decrease. Question 4 2 out of 2 points Fixed cost is the difference between total cost and total variable cost. Question 5 0 out of 2 points The events in an experiment are mutually exclusive if only one can occur at a time. Question 6 2 out of 2 points A continuous random variable may assume only integer values within a given interval. Question 7 2 out of 2 points P(A | B) is the probability of event A, if we already know that event B has occurred. Question 8 2 out of 2 points A BED AND BREAKFAST breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room Question 9 2 out of 2 points EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even Question 10 2 out of 2 points If the price increases but fixed and variable costs do not change, the break even point Question 11 2 out of 2 points The indicator that results in total revenues being equal to total cost is called the Question 12 2 out of 2 points The expected value of the standard normal distribution is equal to Question 13 2 out of 2 points In a binomial distribution, for each of n trials, the event Question 14 2 out of 2 points The area under the normal curve represents probability, and the total area under the curve sums to Question 15 2 out of 2 points Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000. Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 16 2 out of 2 points A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month Note: please report the result as a whole number, rounding if necessary and omitting the decimal point. Question 17 2 out of 2 points A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point. Question 18 2 out of 2 points The variance of the standard normal distribution is equal to __________. Question 19 2 out of 2 points Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration Question 20 0 out of 2 points Wei is considering pursuing an MS in Information Systems degree. She has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Wei will be accepted by at least one of the two universities {Express your answer as a percent. Round (if necessary) to the nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20} MAT540 Week 3 Quiz 2 Latest 2017 March Question 1 2 out of 2 points Probability trees are used only to compute conditional probabilities. Question 2 2 out of 2 points If two events are not mutually exclusive, then P(A or B) = P(A) + P(B) Question 3 2 out of 2 points Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. Question 4 2 out of 2 points The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are. Question 5 0 out of 2 points Both maximin and minimin criteria are optimistic. Question 6 0 out of 2 points The maximin approach involves choosing the alternative with the highest or lowest payoff. Question 7 2 out of 2 points Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret. Question 8 2 out of 2 points Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot. Question 9 2 out of 2 points A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A’s. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A (Round your answer.) Question 10 2 out of 2 points The chi-square test is a statistical test to see if an observed data fit a _________. Question 11 2 out of 2 points Determining the worst payoff for each alternative and choosing the alternative with the best worst is called Question 12 2 out of 2 points A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions. Weather Cold Warm Rainy S1 S2 S3 Bike: A1 10 8 6 Hike: A2 14 15 2 Fish: A3 7 8 9 If the group chooses to minimize their maximum regret, what activity will they choose Question 13 2 out of 2 points A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. Question 14 0 out of 2 points A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions. Weather Cold Warm Rainy S1 S2 S3 Bike: A1 10 8 6 Hike: A2 14 15 2 Fish: A3 7 8 9 What is the conservative decision for this situation Question 15 2 out of 2 points A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years Note: Write your answers with two places after the decimal, rounding off as appropriate. Question 16 2 out of 2 points A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday Note: Write your answers with two places after the decimal, rounding off as appropriate. Question 17 2 out of 2 points A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. If the probability of brisk business is .40, what is the numerical maximum expected value Question 18 0 out of 2 points The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3). What is the numerical value of the maximin Question 19 0 out of 2 points Consider the following decision tree. What is the expected value for the best decision Round your answer to the nearest whole number. Question 20 0 out of 2 points A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions. If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is the EVPI for this situation MAT540 Week 7 Quiz 3 Latest 2017 March Question 1 2 out of 2 points The following inequality represents a resource constraint for a maximization problem: X + Y 20 Question 2 2 out of 2 points In minimization LP problems the feasible region is always below the resource constraints. Question 3 2 out of 2 points In a linear programming problem, all model parameters are assumed to be known with certainty. Question 4 2 out of 2 points If the objective function is parallel to a constraint, the constraint is infeasible. Question 5 2 out of 2 points Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Question 6 2 out of 2 points Surplus variables are only associated with minimization problems. Question 7 2 out of 2 points A feasible solution violates at least one of the constraints. Question 8 2 out of 2 points Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit Question 9 2 out of 2 points The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. This linear programming problem is a: Question 10 2 out of 2 points Which of the following statements is not true Question 11 2 out of 2 points Decision variables Question 12 2 out of 2 points The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used Question 13 2 out of 2 points The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. Which of the following constraints has a surplus greater than 0 Question 14 2 out of 2 points The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The equation for constraint DH is: Question 15 2 out of 2 points Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint Question 16 2 out of 2 points The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint Question 17 2 out of 2 points A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is a maximization, which extreme point is the optimal solution Question 18 2 out of 2 points Max Z = $3x + $9y Subject to: 20x + 32y 1600 4x + 2y 240 y 40 x, y 0 At the optimal solution, what is the amount of slack associated with the second constraint Question 19 2 out of 2 points Consider the following minimization problem: Min z = x1 + 2×2 s.t. x1 + x2 300 2×1 + x2 400 2×1 + 5×2 750 x1, x2 0 Find the optimal solution. What is the value of the objective function at the optimal solution Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Question 20 2 out of 2 points A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB Write your answer in decimal notation. MAT540 Week 9 Quiz 4 Latest 2017 March Question 1 2 out of 2 points When using a linear programming model to solve the “diet” problem, the objective is generally to maximize profit. Question 2 2 out of 2 points Fractional relationships between variables are permitted in the standard form of a linear program. Question 3 2 out of 2 points A constraint for a linear programming problem can never have a zero as its right-hand-side value. Question 4 2 out of 2 points A systematic approach to model formulation is to first construct the objective function before determining the decision variables. Question 5 2 out of 2 points In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories. Question 6 2 out of 2 points In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Question 7 2 out of 2 points The following types of constraints are ones that might be found in linear programming formulations: 1. 2. = 3. > Question 8 2 out of 2 points Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility. What is the demand constraint for plant B Question 9 2 out of 2 points The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit Question 10 2 out of 2 points The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is: Question 11 2 out of 2 points In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is Question 12 2 out of 2 points If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company’s 3 products in period 2 is equal to 400. Question 13 2 out of 2 points The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint Question 14 2 out of 2 points A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today’s production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit Question 15 2 out of 2 points The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50. What is the constraint for salt Question 16 2 out of 2 points A systematic approach to model formulation is to first Question 17 2 out of 2 points Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in “stock two”. The constraint for this requirement can be written as: Question 18 2 out of 2 points Balanced transportation problems have the following type of constraints: Question 19 2 out of 2 points Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How many gallons of water based paint should the Quickbrush make Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate. Question 20 2 out of 2 points Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan Express your answer with two places to the right of the decimal point. For instance, $9.32 (nine dollars and thirty-two cents) would be written as 9.32 MAT540 Week 10 Quiz 5 Latest 2017 March Question 1 2 out of 2 points The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Question 2 2 out of 2 points If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program. Question 3 2 out of 2 points In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 0 implies that if project 2 is selected, project 1 can not be selected. Question 4 2 out of 2 points If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 1 is a mutually exclusive constraint. Question 5 2 out of 2 points A conditional constraint specifies the conditions under which variables are integers or real variables. Question 6 2 out of 2 points Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Question 7 2 out of 2 points Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 2) means that __________ out of the 4 projects must be selected. Question 8 2 out of 2 points The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Selected Answer: Correct Y1 + Y4 1 Correct Answer: Correct Y1 + Y4 1 Question 9 2 out of 2 points You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction Question 10 2 out of 2 points Binary variables are Question 11 2 out of 2 points You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, the constraint for the first restriction is Question 12 2 out of 2 points The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Write the constraint that indicates they can purchase no more than 3 machines. Question 13 2 out of 2 points In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected. Question 14 2 out of 2 points In a 0-1 integer programming model, if the constraint x1-x2 0, it means when project 2 is selected, project 1 __________ be selected. Question 15 2 out of 2 points Max Z = 5×1 + 6×2 Subject to: 17×1 + 8×2 136 3×1 + 4×2 36 x1, x2 0 and integer What is the optimal solution Question 16 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Question 17 2 out of 2 points In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Question 18 0 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Question 19 2 out of 2 points Max Z = 3×1 + 5×2 Subject to: 7×1 + 12×2 136 3×1 + 5×2 36 x1, x2 0 and integer Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25 Question 20 0 out of 2 points Consider the following integer linear programming problem Max Z = 3×1 + 2×2 Subject to: 3×1 + 5×2 30 5×1 + 2×2 28 x1 8 x1 ,x2 0 and integer Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25
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