San Diego State University Operations And Supply Chain Management Assignment Help - Optimal

Question - 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 m ...Read More inutes 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:
Min10AM + 6AM + 14AP + 9BP
s.t.
1AM + + 1AP + = 100Demand for model A
1BM + 1BP = 150Demand for model B
4AM + 3BM = 600Injection molding time
6BM + 8BM = 1080Assembly time
AM, BM, AP, BP ?Y 0
The computer solution developed using The Management Scientist is shown in Figure.
THE MANAGEMENT SCIENTIST SOLUTION FOR THE DIGITAL CONTROLS, INC., PROBLEM

a. W hat is the optimal solution and what is the optimal value of the objective function?
b. W hich constraints are binding?
c. What are the dual prices? Interpret each.
d. If you could change the right-hand side of one constraint by one unit, which one would you
choose?Why? ...Read Less

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