Quantitative Models for Decision-Makers Management MCQ Paper

Quantitative Models for Decision-Makers
There are 13 Multiple choices and 2 file in blank question in the attachment.
Please answer them correctly and as soon as possible.

Quantitative Models for Decision-Makers

1. 1.      Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $100 and farmhouse style cabinets sell for $150. Each cabinet produced must go through carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.

Carpentry costs $10 per hour, painting costs $20 per hour, and finishing costs $15 per hour, and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 500 contemporary cabinets and 650 farmhouse style cabinets each week.

Q: What is the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit?

• A. 15.0x + 5.0y 
• B. 11.1x + 21.4y
• C. 5x + 15y
• D. 5.5x + 15.5y

1. 2.      Solve the following linear program to find the:

Q: What is the optimal solution value?

Min     8X + 16Y

s.t.       3X + Y    ≥ 10

              X +2Y   ≥ 15

           3X + 2Y   ≥ 12

                 X, Y     ≥ 0

• A.  130
• B. 125
• C. 120
• D. 115

1. 3.      Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2,000 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 150 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 1,200 hours of assembly and testing time are available for the next production period. The company’s accounting department projects a profit contribution of $2,000 for each EZ-Rider produced and $2,500 for each Lady-Sport produced.

Q: What is the optimal solution?

• A. $90,1666.67
• B. $89,500.50
• C. $90,150.67
• D. $89,1666.67

1. 4.      Consider the following linear program:

Min   250X + 300Y

s.t.     2X  + 4Y    ≥ 11

          3X  + 3Y    ≥ 17

          4X  + 3Y    ≥ 21

            X, Y     ≥ 0

Assume that the objective function coefficient for X changes from 250 to 200, and the objective function coefficient for Y changes from 300 to 400.

Q: What is the value change of optimal solution?

• A. 263
• B. 283
• C. 233
• D. 238

1. 5.      Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $90 per share and the annual return for Huber Steel is $100 per share. U.S. Oil sells for $31 per share and Huber Steel sells for $42 per share. The portfolio has $60,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.50 per share for Huber Steel) has a maximum of 1,300. In addition, the portfolio is limited to a maximum of 20,000 shares of U.S. Oil.

Q: What is the optimal solution, and what is the value of the total annual return (rounded)?

• A. $150,200
• B. $174,200
• C. $8,700
• D. $5,600

1. 6.      Grant Energy Producers supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in New York, Virginia, and Kentucky. The following table shows Grant Energy Producers’ major residential markets, the annual demand in each market (in megawatts or MW), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).

Q: If there are no restrictions on the amount of power that can be supplied by any of the power plants, what is the optimal solution to this problem?

• A. 1,150,000
• B. 1,250,000
• C. 1,200,000
• D. 1,300,000

1. 7.      Grant Energy Producers supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in New York, Virginia, and Kentucky. The following table shows Grant Energy Producers’ major residential markets, the annual demand in each market (in megawatts or MW), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).

Q: If at most 1,500 MW of power can be supplied by any one of the power plants, what is the optimal solution?

• A. 1,650,000
• B. 1,550,000
• C. 1,450,000
• D. 1,600,000

1. 8.      At a local university, the Student Commission on Programming and Entertainment (SCOPE) is preparing to host its first rock concert of the school year. To successfully produce this rock concert, SCOPE has listed the requisite activities and related information in the following table (duration estimates measured in days).

Q: What is the critical path in the project network.

• A. A-C-E-G
• B. A-C-F-G
• C. A-D-F-G
• D. A-D-E-G

1. 9.      Hale’s TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network’s decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale’s decision alternatives and profits (in thousands of dollars) are as follows:

The probabilities for the states of nature are P(S1) = 0.20, P(S2) = 0.30, and P(S3) = 0.50. For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant:

P(F) = 0.69        P(S1 | F) = 0.09    P(S1 | U) = 0.45
P(U) = 0.31        P(S2 | F) = 0.26    P(S2 | U) = 0.39
                          P(S3 | F) = 0.65    P(S3 | U) = 0.16

Q: What is the recommended decision if the agency opinion is not used? What is the expected value?

• A. Buy, $150
• B. Sell, $100
• C. Sell, $150
• D. Buy, $100

10.  The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

The credit union will have $2 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

• Risk-free securities may not exceed 30% of the total funds available for investments.
• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

Q: What is the projected total annual return?

• A. $188,800
• B. $177,700
• C. $199,900
• D. $166,600

11.  Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table:

If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the minimax regret approach?

• A. d₂ 
• B. d₄
• C. d₁
• D. d₃

1. 12.    

What follows is a fill in the blank question with 2 blanks.

 Blank 1. Fill in the blank, read surrounding text. 

(            )variable is added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resource.

 Blank 2. Fill in the blank, read surrounding text. 

(            )variable is subtracted from the left-hand side of a greater-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level.  

13.  Consider the following three-state, three-decision problem with the following payoff table in dollars:

Probabilities for states of nature changed to: P(S₁) = .2, P(S₂) = .4, P(S₃) = .6

Q: Which decision d_x provides the maximum optimal value?

• A. All d_x are the same value.
• B. d₁
• C. d₃
• D. d₂

14.  (          )is added to a transportation problem to make the total supply equal to the total demand. 

15.  Linear Programming is a problem-solving approach developed for situations involving maximizing or minimizing a linear function subject to linear constraints that limit the degree to which the objective can be pursued.