Question: MGT 355 Examination

Answer all 5 questions. All work must be shown to qualify for partial credit. You are allowed to use Excel for the forecasting problems. Due Date on or before March 25, 2017.

1. The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives:

Decision Alternatives                       State of Nature
                                                  S1               S2
D1                                               10                1
D2                                                4                 3

a. Use graphical sensitivity analysis to determine the range of probabilities of state of nature S1 for which each of the decision alternatives has the largest expected value.

b. Suppose P(S1) = 0.2 and P(S2) = 0.8. What is the best decision using the expected value approach?

c. Perform sensitivity analysis on the payoffs for decision alternative D1. Assume the probabilities are as given in part (b) and the range of payoffs under states of nature S1 and S2 that will keep the solution found in part (b) optimal. Is the solution more sensitive to the payoff under state of nature S1 or S2?

2. The monthly sales for Telco Batteries, Inc., were as follows in Table 1:
Table 1: Monthly Sales
MONTH                 SALES
January                   10
February                  14
March                     15
April                       14
May                       12
June                      10
July                       14
August                   18
September              20
October                  20
November                22
December                23

Forecast January sales using each of the following:

a) A 3-month moving average.

b) Exponential smoothing using an alpha = 0.25

c) Use Trend projection model to generate the forecast.

d) Which of these forecast models is the best and why?

3.
                         Destination

Origin           Boston          Chicago         St. Louis         Lexington          Supply

Cleveland         3                 2                   7                   6                 5000

Bedford           7                 5                   2                   3                  6000

York               2                 5                   4                   5                  2500

Trenton          4                 6                   2                   3                  2500

Demand             6500        5000         2500         2000

The above table presents a transportation cost matrix for distribution of goods from the demand centers known as the Origin to the Supply Centers known as the Destination. Develop a linear programming formulation of this problem and find the optimal solution for the transportation problem. You must use Excel Solver to solve this problem.

4. Consider the following all-integer linear program:

Min 1x1 + 2x2

s.t.
1x₁ + 4x₂ < 21
2x₁ + 1x₂ > 7
3x₁ + 1.5x₂ < 21
-2x₁ + 6x₂ > 0

x1, x2> 0

a. Graph the constraints for this problem.

b. Solve the LP problem and identify the feasible region, corner point solutions, and the optimal solution.

c. Suppose the objective function is changed to max 5x1 + 2x2. Find the optimal solution and the value of the objective function.