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 1,080 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 + 1BM + 4AM + 3BM + 1AP + = 100 1BP = 150 600 1,080 6AM + 8BM AM, BM, AP, BP 0 Refer to the computer solution below. Optimal Objective Value 2170.00000 Variable AB Value 100.00000 Reduced Cost 0.00000 BM 60.00000 0.00000 AP 0.00000 1.75000 90.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 2 0.00000 -12.25000 -9.00000 3 20.00000 4 0.00000 0.00000 0.37500 Demand for model A Demand for model B Injection molding time Assembly time Objective Allowable Allowable Variable Coefficient. Increase Decrease ! AB BM AP 10.00000 6.00000 14.00000 9.00000 1.75000 3.00000 Infinite 2.33333 Infinite 2.33333 1.75000 3.00000 Constraint RHS Value 1234 100.00000 Allowable Increase 11.42857 Allowable Decrease 100.00000 150.00000 600.00000 1,080.00000 Infinite Infinite 53.33333 90.00000 20.00000 480.00000