Q1: Problem 14

Digital Controls, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus 3 miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time available and 1080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time available at the Newark plant, DCI occasionally purchases cases for one or both models from an outside supplier in order to fill customer orders that could not be filled otherwise. The purchase cost is $14 for each model A case and $9 for each model B case. Management wants to develop a minimum cost plan that will determine how many cases of each model should be produced at the Newark plant and how many cases of each model should be purchased. The following decision variables were used to formulate a linear programming model for this problem:

AM = number of cases of model A manufactured
BM = number of cases of model B manufactured
AP = number of cases of model A purchased
BP = number of cases of model B purchased

The linear programming model that can be used to solve this problem is as follows:

Min                 10AM + 6BM + 14AP + 9BP

s.t.                     1AM +               +  1AP                         =100    Demand for model A

               1BM              + 1BP       =150 Demand for model B
  4AM + 3BM                                    ≤ 600 Injection molding time
  6AM + 8BM                            ≤1080 Assembly time

AM, BM, AP, BP ≥ 0

The computer solution is shown in Figure 3.18. However, I would like you to produce the Solver and LINGO output by yourself.

            •            Please snipping your Solver and LINGO output below.

1.2 What is the optimal solution, and what is the minimum total cost?

a. 100, 150, 600, 1080; 2170

b. 100, 150, 580, 1080; 2170

c. 100, 60, 0, 90; 2170

1.3 Which constraints are not binding?

a. Constraint 1, 2, 4

b. Constraint 3

c. Constraint 1, 2, 3, 4

1.4 How many Reduced Cost that we can apply for in the optimal solution?

a. 2

b. 1

c. 0

1.5 An additional unit purchased for AP will reduce or decrease the cost by how much (reduced cost)?

a. Increase; 1.75

b. Increase; 0

c. Reduce; 1.75

d. Reduce; 0

1.6 What is the slack for constraint 3 – Injection molding time?

a. 20

b. 0

1.7 What is the allowable range for coefficient BM (range of optimality)?

a. Infinite to 11.75

b. 57.6667 to 63

c. 3.6667 to 9

1.8 What is the dual value or shadow price for constraint 2 – Demand for Model B?

a. 12.25

b. 9

c. -0.375

1.9 For constraint 4 – Assembly time, an additional assemble time will increase or reduce the cost by how much?

a. Increase; 12.25

b. Increase; 0.375

c. Reduce; 12.25

d. Reduce; 0.375

1.10 Determine the range of right-hand-side values with allowable increase/decrease which the dual value or shadow price would be valid for constraint 1 – Demand for model A (Range of feasibility)?

a. 600 to 1133.33

b. 60 to infinite

c. 0 to 111.42

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