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##### Strayer MAT540 final exam (2014)

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Question;Question 1;In a transshipment problem, items may be transported from destination to;destination and from source to source.;Answer;True;False;Question 2;In a total integer model, all decision variables have integer solution;values.;Answer;True;False;Question 3;In an unbalanced transportation model, supply does not equal demand and;one set of constraints uses? signs.;Answer;True;False;Question 4;If we are solving a 0-1 integer programming problem, the;constraint x1 = x2 is a conditional;constraint.;Answer;True;False;uestion 5;Fractional relationships between variables are not permitted in the;standard form of a linear program.;Answer;True;False;Question 5;Fractional relationships between variables are not permitted in the;standard form of a linear program.;Answer;True;False;Question 6;Excel can be used to simulate systems that can be represented by both;discrete and continuous random variables.;Answer;True;False;Question 7;The probability of observing x;successes in a fixed number of trials is a problem related to;Answer;the normal distribution;the;binomial distribution;conditional probability;the Poisson distribution;Question 8;Using the maximin criterion to make a decision, you;Answer;Construct a table of regrets. Look at the;maximum regret for each decision. Select the decision with the smallest;maximum regret.;Look at the worst payoff for each possible;decision and select the decision with the largest worst payoff;Look at;the best payoff for each possible decision and select the decision with the;largest best payoff;Consult an astrological table to forecast the;state of nature;Question 9;Using the minimax regret criterion to make a decision, you;Answer;Construct a table of regrets. Look at the;maximum regret for each decision. Select the decision with the smallest;maximum regret.;Look at the worst payoff for each possible;decision and select the decision with the largest worst payoff;Construct;a table of regrets. Look at the minimum regret for each decision.;Select the decision with the smallest minimum regret.;Run in circles, scream and shout;Question 10;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.;The conservative (maximin) strategy is;Answer;Buy;Rent;Lease;Brisk.;Question 11;An equation or inequality that expresses a resource restriction in a;mathematical model is called _____________________.;Answer;a decision variable.;a parameter.;an objective function.;a constraint.;Question 12;Steinmetz 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.In;order to maximize profit, how many big shelves (B) and how many medium shelves;(M) should be purchased?;Answer;B = 225, M;= 0;B = 0, M = 225;B = 150, M = 75;B = 75, M = 150;Question 13;Steinmetz 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?;Answer;Max Z = 75B + 85M;100B + 50M? 25000;100B +;80M? 18000;100B + 80M = 18000;5 points;Question 14;For a maximization problem, assume that a constraint is binding. If the;original amount of a resource is 4 lbs., and the range of feasibility;(sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing;the amount of this resource by 1 lb. will result in the;Answer;same;product mix, different total profit;different product mix, same total profit as;before;same product mix, same total profit;different product mix, different total;profit;Question 15;The 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?;Answer;mix/mold;kiln;paint and seal;Cannot tell from the information provided;Question 16;Let 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.;Answer;x11 + x21? 8000;x12 + x21? 8000;x11 +;x12? 8000;x11 + x12? 8000;Question 17;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.;An appropriate part of the model would be;Answer;15X1 +;47.25X2 +110 X3? 50,000;MAX Z =15X1 + 47.25X2 + 110X3;X1 + X2 +X3? 50,000;MAX Z = 50(15)X1 + 50;(47.25)X2 + 50 (110)X3;Question 18;If we are solving a 0-1 integer programming problem, the;constraint x1 = x2 is a;constraint.;Answer;multiple choice;mutually exclusive;conditional;corequisite;Question 19;The 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 the constraint that indicates they have to use at least three of;the five machines in their production.;Answer;Y1 + Y2 + Y3 + Y4;+ Y5? 3;Y1 + Y2 + Y3 + Y4;+ Y5 = 3;Y1 + Y2 + Y3 + Y4;+ Y5? 3;none of the above;Question 20;The assignment problem constraint x31+x32+x33+x34? 2 means;Answer;agent 3;can be assigned to 2 tasks;agent 3 can be assigned to no more than 2 tasks;a mixture of agents 1, 2, 3 and 4 will be;assigned to tasks;agent 2 can be assigned to 3 tasks;Question 21;The 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 demanded by Customer B is;Answer;6X1B + 2X2B + 8X3B? 350;6X1B + 2X2B + 8X3B = 350;X1B + X2B + X3B? 350;X1B +;X2B + X3B = 350;Question 22;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. What percentage of;the students will take between 2 and 6 minutes to find a parking spot in the;main parking lot?;Answer;11.13%;47.72%;43.32%;62.47%;Question 23;Jack is considering pursuing an MS in Information Systems degree. He has;applied to two different universities. The acceptance rate for applicants with;similar qualifications is 30% for University X and 60% for University Y. The;decisions of each university have no effect on each other. This means;that they are;Answer;mutually exclusive;independent;controlled by the central limit theorem;all of the above;Question 24;A bakery is considering hiring another clerk to better serve;customers. To help with this decision, records were kept to determine how;many customers arrived in 10-minute intervals. Based on 100 ten-minute;intervals, the following probability distribution and random number assignments;developed.;Number of Arrivals;Probability;Random numbers;6;.1;.01 -.10;7;.3;.11 -.40;8;.3;.41 -.70;9;.2;.71 -.90;10;.1;.91 -.00;Suppose the next three random numbers were.18,.89 and.67. How many;customers would have arrived during this 30-minute period?;Answer;23;24;22;25;uestion 25;For the following frequency distribution of demand, the random number;0.8177 would be interpreted as a demand of;Answer;0;1;2;3;Question 26;Given an actual demand of 59, a previous forecast of 64, and an alpha of;.3, what would the forecast for the next period be using simple exponential;smoothing?;Answer;36.9;57.5;60.5;62.5;uestion 27;Consider the following graph of sales.;Which of the following characteristics is exhibited by the data?;Answer;Trend only;Trend plus seasonal;Trend plus;irregular;Seasonal;Question 28;Students 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).;Answer;Question 29;Carter?s Bed & Breakfast breaks even every month if they book 30;rooms over the course of a month. Their fixed cost is $1050 per month and;the revenue they receive from each booked room is $150. What is the;variable cost per occupied 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 $105.00).;Answer;Question 30;Joseph is considering pursuing an MS in Information Systems degree. He;has applied to two different universities. The acceptance rate for applicants;with similar qualifications is 30% for University X and 60% for University Y.;What is the probability that Jim will not be accepted at either;university? (Note: write your answer as a;probability, with two decimal places. If necessary, round to two decimal;places. For instance, a probability of 0.252 should be written as;0.25).;Question 31;Consider the following linear program, which maximizes profit for two;products, regular (R), and super (S);MAX;50R + 75S;s.t.;1.2R +;1.6 S? 600 assembly (hours);0.8R +;0.5 S? 300 paint (hours);.16R +;0.4 S? 100 inspection (hours) Sensitivity Report;Final;Reduced;Objective;Allowable;Allowable;Cell;Name;Value;Cost;Coefficient;Increase;Decrease;$B$7;Regular =;291.67;0.00;50;70;20;$C$7;Super =;133.33;0.00;75;50;43.75;Final;Shadow;Constraint;Allowable;Allowable;Cell;Name;Value;Price;R.H. Side;Increase;Decrease;$E$3;Assembly (hr/unit);563.33;0.00;600;1E+30;36.67;$E$4;Paint (hr/unit);300.00;33.33;300;39.29;175;$E$5;Inspect (hr/unit);100.00;145.83;100;12.94;40;A 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.;Question 32;Consider the following linear program, which maximizes profit for two;products, regular (R), and super (S);MAX;50R + 75S;s.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;Final;Reduced;Objective;Allowable;Allowable;Cell;Name;Value;Cost;Coefficient;Increase;Decrease;$B$7;Regular =;291.67;0.00;50;70;20;$C$7;Super =;133.33;0.00;75;50;43.75;Final;Shadow;Constraint;Allowable;Allowable;Cell;Name;Value;Price;R.H. Side;Increase;Decrease;$E$3;Assembly (hr/unit);563.33;0.00;600;1E+30;36.67;$E$4;Paint (hr/unit);300.00;33.33;300;39.29;175;$E$5;Inspect (hr/unit);100.00;145.83;100;12.94;40;If downtime reduced the available capacity for painting by 40 hours (from 300;to 260 hours), profits would be reduced by __________. Write your answers with;two significant places after the decimal and do not include the dollar ?$?;sign.;Question 33;Kalamazoo 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 Food;Cost/oz;protien (%);fat (%);Pet's;Choice;0.35;40;15;Feline;Chow;0.32;20;30;Kalamazoo 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;$9.45 (nine dollars and fortyfive cents) should be written as 9.45;Answer;Question 34;Find the optimal Z value for the following problem. Do not include the;dollar ?$? sign with your answer.;MAX Z = 5x1 + 8x2;s.t.;x1 + x2? 6;5x1 + 9x2? 45;x1, x2? 0 and integer;Answer;uestion 35;Let us take as a given that x is normally distributed with a mean of 8.5;and a standard deviation of 2, what is P(x? 6)? Note: Round;your answer, if necessary, to two places after the decimal. Please;express your answer with two places after the decimal.;Answer;Question 36;Ms. 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.;Investment;Economic Conditions;Poor;(S1);Average;(S2);Good;(S3);Excellent;(S4);A;80;15;18;47;B;50;75;35;35;C;-90;225;-50;12;D;36;25;25;27;Suppose 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;applicable;Answer;Question 37;The 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 = $50,000). Round to the nearest;whole number, if necessary.;Question 38;The local operations manager for the IRS must decide whether to hire 1;2, or 3 temporary workers. He estimates that net revenues will vary with how;well taxpayers comply with the new tax code. The probabilities of low, medium;and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected;value of perfect information? Do not include the dollar ?$? 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 = $50,000). Round to the nearest;whole number, if necessary.;Question 39;Recent past demand for product ABC is given in the following table.;Month;Actual Demand;May;33;June;32;July;39;August;37;The forecasted demand for May, June, July and August were 25, 30, 33, and;38 respectively. Determine the value of MAD. Note: Please express;the result as a number with 2 decimal places. If necessary, round your;result accordingly. For instance, 9.146, should be expressed as 9.15;Answer;4.25;Question 40;Consider the following decision tree. The objective is to choose the;best decision among the two available decisions A and B. Find the expected;value of the best decision. Do not include the dollar ?$? sign with your;answer.;Answer

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