Mat 540 Quantitative Methods Final Exam.docx

Mat 540 Quantitative Methods Final E Mat 540 Quantitative Methods Final ExamQuestion 15 out of 5 pointsCorrectIn an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.AnswerSelected Answer: Answer: 25 out of 5 pointsCorrectIn a transshipment problem, items may be transported from destination to destination and from source to source.AnswerSelected Answer: TrueCorrect Answer: 30 out of 5 pointsIncorrectAdjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.AnswerSelected Answer: TrueCorrect Answer: 45 out of 5 pointsCorrectA cycle is an up and down movement in demand that repeats itself in less than 1 year.AnswerSelected Answer: FalseCorrect Answer: FalseQuestion 55 out of 5 pointsCorrectIf we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.AnswerSelected Answer: FalseCorrect Answer: FalseQuestion 65 out of 5 pointsCorrectFractional relationships between variables are not permitted in the standard form of a linear program.AnswerSelected Answer: TrueCorrect Answer: TrueQuestion 75 out of 5 pointsCorrectA 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.The conservative (maximin) strategy is:AnswerSelected Answer:LeaseCorrect Answer:LeaseQuestion 85 out of 5 pointsCorrectEvents that cannot occur at the same time in any trial of an experiment are:AnswerSelected Answer:mutually exclusiveCorrect Answer:mutually exclusiveQuestion 95 out of 5 pointsCorrectThe probability of observing xsuccesses in a fixed number of trials is a problem related toAnswerSelected Answer:the binomial distributionCorrect Answer:the binomial distributionQuestion 105 out of 5 pointsCorrectAn equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.AnswerSelected Answer:a constraint.Correct Answer:a constraint.Question 115 out of 5 pointsCorrectIn a break-even model, if all of the costs are held constant, how does an increase in price affect the model?AnswerSelected Answer:Breakeven point decreasesCorrect Answer:Breakeven point decreasesQuestion 125 out of 5 pointsCorrectSteinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint?AnswerSelected Answer:100B 80M ≤ 18000Correct Answer:100B 80M ≤ 18000Question 135 out of 5 pointsCorrectSteinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?AnswerSelected Answer:100B 50M ≤ 25000Correct Answer:100B 50M ≤ 25000Question 145 out of 5 pointsCorrectGiven the following linear programming problem that minimizes cost.Min Z = 2x 8ySubject to 8x 4y ≥ 642x 4y ≥ 32y ≥ 2What is the sensitivity range for the third constraint, y ≥ 2?AnswerSelected Answer:0 to 5.33Correct Answer:0 to 5.33Question 155 out of 5 pointsCorrectThe following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem:The Answer Report:The Sensitivity Report:Which additional resources would you recommend to be increased?AnswerSelected Answer:kilnCorrect Answer:kilnQuestion 165 out of 5 pointsCorrectLet xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.AnswerSelected Answer:x11 x12 ≤ 8000Correct Answer:x11 x12 ≤ 8000Question 175 out of 5 pointsCorrectCompared to transportation LP problems, assignment problems are unique becauseAnswerSelected Answer:Both of the aboveCorrect Answer:Both of the aboveQuestion 185 out of 5 pointsCorrectThe Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.AnswerSelected Answer:Y1 Y4 ≤ 1Correct Answer:Y1 Y4 ≤ 1Question 195 out of 5 pointsCorrectIf we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.AnswerSelected Answer:corequisiteCorrect Answer:corequisiteQuestion 205 out of 5 pointsCorrectConsider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6?AnswerSelected Answer:X36 X26 ≤ 450Correct Answer:X36 X26 ≤ 450Question 215 out of 5 pointsCorrectThe following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C.The constraint that represents the quantity supplied by DC 1 is:AnswerSelected Answer:X1A X1B X1C ≤ 500Correct Answer:X1A X1B X1C ≤ 500Question 225 out of 5 pointsCorrectProfessor Truman would like to assign grades such that 10% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)AnswerSelected Answer:79Correct Answer:79Question 235 out of 5 pointsCorrectAssume 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. What percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot?AnswerSelected Answer:62.47%Correct Answer:62.47%Question 245 out of 5 pointsCorrectIn the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.AnswerSelected Answer:sampling fromCorrect Answer:sampling fromQuestion 255 out of 5 pointsCorrectFor the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:AnswerSelected Answer:2Correct Answer:2Question 265 out of 5 pointsCorrectConsider the following graph of sales.Which of the following characteristics is exhibited by the data?AnswerSelected Answer:Trend plus irregularCorrect Answer:Trend plus irregularQuestion 275 out of 5 pointsCorrect__________ moving averages react more slowly to recent demand changes than do __________ moving averages.AnswerSelected Answer:Longer-period, shorter-periodCorrect Answer:Longer-period, shorter-periodQuestion 285 out of 5 pointsCorrectStudents are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “$” sign. For instance, for five dollars, write your answer as 5.00).AnswerSelected Answer: 7.00Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 7.00Question 290 out of 5 pointsIncorrectNixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200. The variable cost per room is $75. How many rooms do they have to sell each month to break even? (Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms).AnswerSelected Answer: 3Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 40Question 305 out of 5 pointsCorrectFord’s Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of $6500 per month. The variable cost per room is $30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00).AnswerSelected Answer: 160Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 160Question 315 out of 5 pointsCorrectConsider the following linear program, which maximizes profit for two products, regular (R), and super (S):MAX50R 75Ss.t.1.2R 1.6 S ≤ 600 assembly (hours)0.8R 0.5 S ≤ 300 paint (hours).16R 0.4 S ≤ 100 inspection (hours)Sensitivity Report:FinalReducedObjectiveAllowableAllowableCellNameValueCostCoefficientIncreaseDecrease$B$7Regular =291.670.$C$7Super =133.330..75FinalShadowConstraintAllowableAllowableCellNameValuePriceR.H. SideIncreaseDecrease$E$3Assembly (hr/unit)563.330.E 3036.67$E$4Paint (hr/unit)300.0033..29175$E$5Inspect (hr/unit)100.00145..9440A change in the market has increased the profit on the super product by $5. Total profit will increase by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.AnswerSelected Answer: 667Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 667Question 325 out of 5 pointsCorrectConsider the following linear program, which maximizes profit for two products, regular (R), and super (S):MAX50R 75Ss.t.1.2R 1.6 S ≤ 600 assembly (hours)0.8R 0.5 S ≤ 300 paint (hours).16R 0.4 S ≤ 100 inspection (hours)Sensitivity Report:FinalReducedObjectiveAllowableAllowableCellNameValueCostCoefficientIncreaseDecrease$B$7Regular =291.670.$C$7Super =133.330..75FinalShadowConstraintAllowableAllowableCellNameValuePriceR.H. SideIncreaseDecrease$E$3Assembly (hr/unit)563.330.E 3036.67$E$4Paint (hr/unit)300.0033..29175$E$5Inspect (hr/unit)100.00145..9440If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by __________. Write your answers with two significant places after the decimal and do not include the dollar “$” sign.AnswerSelected Answer: 1333Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 1333Exact Match 1,333Question 330 out of 5 pointsIncorrectKitty 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:Cat FoodCost/ozprotien (%)fat (%)Meow Munch$0.Feline Feed$0.Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$” sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45AnswerSelected Answer: 2.50Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 3.60Question 345 out of 5 pointsCorrectFind the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer.Max Z = x1 6x2Subject to: 17x1 8x2 ≤ 1363x1 4x2 ≤ 36x1, x2 ≥ 0 and integerAnswerSelected Answer: 54Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 54Question 355 out of 5 pointsCorrectLet’s say that 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 72 years and a standard deviation of 5 years. What proportion of the plan participants are expected to survive to see their 75thbirthday? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.AnswerSelected Answer: 0.27Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 0.27Exact Match .27Question 365 out of 5 pointsCorrectMs. Hegel is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.InvestmentEconomic ConditionsPoor(S1)Average(S2)Good(S3)Excellent(S4)ABC-DSuppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicableAnswerSelected Answer: 48Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 48Question 375 out of 5 pointsCorrectThe local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.AnswerSelected Answer: 26Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 26Question 385 out of 5 pointsCorrectThe local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.AnswerSelected Answer: 50Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 50Question 390 out of 5 pointsIncorrectRecent past demand for product ABC is given in the following table.MonthActual DemandMay33June32July39August37The forecasted demand for May, June, July and August were 25, 30, 33, and 38 respectively. Determine the value of MAD. Note: Please express the result as a number with 2 decimal places. If necessary, round your result accordingly. For instance, 9.146, should be expressed as 9.15AnswerSelected Answer: 7.3061Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 4.25Question 405 out of 5 pointsCorrectConsider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$” sign with your answer.AnswerSelected Answer: 2100Correct Answer:Evaluation Method Correct Answer Case SensitivityExact Match 2100Exact Match 2,100