** **

**In-Class Practice Quiz Three**

1) The maximax criterion results in the

- A) maximum of the minimum payoffs.
- B) maximum of the maximum payoffs.
- C) minimum of the maximum payoffs.
- D) minimum of the minimum payoffs.

2) Regret is the difference between the payoff from the

- A) best decision and all other decision payoffs.
- B) worst decision and all other decision payoffs.
- C) best decision and the worst decision payoffs.
- D) none of the above

3) The ________ minimizes the maximum regret.

- A) maximax regret criterion
- B) minimax regret criterion
- C) minimin regret criterion
- D) maximin regret criterion

4) In a transportation problem, items are allocated from sources to destinations

- A) at a maximum cost.
- B) at a minimum cost.
- C) at a minimum profit.
- D) at a minimum revenue.

5) The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination.

- A) destination, source
- B) source, destination
- C) demand, source
- D) source, demand

6) Which of the following assumptions is not an assumption of the transportation model?

- A) Shipping costs per unit are constant.
- B) There is one transportation route between each source and destination.
- C) There is one transportation mode between each source and destination.
- D) Actual total supply and actual total demand must be equal.

7) The maximin approach to decision making refers to

- A) minimizing the maximum return.
- B) maximizing the minimum return.
- C) maximizing the maximum return.
- D) minimizing the minimum return.

8) In a linear programming problem, the binding constraints for the optimal solution are:

5*x*1 + 3*x*2 ≤ 30

2*x*1 + 5*x*2 ≤ 20

(The optimal solution occurs at their intersection)

Which of these objective functions would lead to the same optimal solution?

- A) 2
*x*1+ 1*x*2 - B) 7
*x*1+ 8*x*2 - C) 80
*x*1+ 60*x*2 - D) 25
*x*1+ 15*x*2

9) Decision variables

- A) measure the objective function.
- B) measure how much or how many items to produce, purchase, hire, etc.
- C) always determine the values that maximize profit.
- D) measure the values of each constraint.

10) A linear programming model consists of

- A) decision variables.
- B) an objective function.
- C) constraints.
- D) all of the above

11) Which of the following could be a linear programming objective function?

- A) Z = 1A + 2BC + 3D
- B) Z = 1A + 2B + 3C + 4D
- C) Z = 1A + 2B / C + 3D
- D) Z = 1A + 2B2+ 3D

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon’s ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.

School |
Scenario 1 |
Scenario 2 |
Scenario 3 |

Vanderbilt | 95 | 20 | -10 |

Texas Tech | 55 | 60 | 60 |

Seattle | 90 | 10 | 80 |

Northeastern State | 65 | 50 | 60 |

- Under which decision-making criterion is Vanderbilt University the optimal choice?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely

- Under which decision-making criterion is Texas Tech University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely

- Under which criterion is Seattle University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely

- Under which criterion is Northeastern State University the optimal decision?
- A) maximax
- B) maximin
- C) minimax regret
- D) equally likely

- Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 0.4, and 0.3, respectively. What is the optimal decision under the expected opportunity loss criterion?
- A) Vanderbilt University
- B) Texas Tech University
- C) Seattle University
- D) Northeastern State University

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets.

**V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing **

** **

17) What is the distance for the shortest route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois.

- A) 36
- B) 37
- C) 39
- D) 41

18) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso to retail outlet in Hammond.

- A) 26
- B) 28
- C) 30
- D) 32

** **

** **

19) Consider the network diagram below. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes?

- A) 16 miles
- B) 17 miles
- C) 18 miles
- D) 19 miles

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

20) Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility?

- A) 54
- B) 56
- C) 60
- D) 65

21) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9.

** **

** **

** **

- A) 10
- B) 11
- C) 12
- D) 13

22) In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 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:

- A) 15X1+ 47.25X2 +110 X3 ≤ 50,000
- B) MAX 15X1+ 47.25X2 + 110X3
- C) X1+ X2 +X3 ≤ 50,000
- D) MAX 50(15)X1+ 50 (47.25)X2 + 50 (110)X3

23) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is:

- A) MAX .06X1+.08X2 +.11X3
- B) MAX .06(15)X1+.08(47.25)X2 +.11(110)X3
- C) MAX 15X1+ 47.25X2 +.110X3
- D) MAX (1/.06)X1+.(1/08)X2 + (1/.11)X3

24) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?

- A) X1≤ 0.35
- B) X1= 0.35 (50000)
- C) X1 ≤ 35(X1+ X2 + X3)
- D) X1 = 35(X1+ X2 + X3)

25) In a balanced transportation model where supply equals demand,

- A) all constraints are equalities.
- B) none of the constraints are equalities.
- C) all constraints are inequalities.
- D) none of the constraints are inequalities.

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to

Customer A, B, or C.

26) The constraint that represents the quantity supplied by DC 1 is:

- A) 4X1A + 6X1B+ 8X1C≤ 500
- B) 4X1A + 6X1B+ 8X1C= 500
- C) X1A + X1B+ X1C≤ 500
- D) X1A + X1B+ X1C=500

27) The constraint that represents the quantity demanded by Customer B is:

- A) 6X1B + 2X2B+ 8X3B≤ 350
- B) 6X1B + 2X2B+ 8X3B= 350
- C) X1B + X2B+ X3B≤ 350
- D) X1B + X2B+ X3B= 350