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 for100 unitsof model A and150 unitsof 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 and6 minutesof assembly time. Each model B case requires 3 minutes of injection-molding time and8 minutesof assembly time. For next week, the Newark plant has600 minutesof injection-molding time available and1,080 minutesof 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+6BM+14AP+9BPs.t.1AM++1AP+=100Demand for model A1BM+1BP=150Demand for model B4AM+3BM600Injection molding time6AM+8BM1,080Assembly time

AM,BM,AP,BP0

Refer to the computer solution below.

Optimal Objective Value = 2170.00000

VariableValueReduced CostAB100.000000.00000BM60.000000.00000AP0.000001.75000BP90.000000.00000ConstraintSlack/SurplusDual Value10.0000012.2500020.000009.00000320.000000.0000040.000000.37500VariableObjective

CoefficientAllowable

IncreaseAllowable

DecreaseAB10.000001.75000InfiniteBM6.000003.000002.33333AP14.00000Infinite1.75000BP9.000002.333333.00000ConstraintRHS

ValueAllowable

IncreaseAllowable

Decrease1100.0000011.42857100.000002150.00000Infinite90.000003600.00000Infinite20.0000041,080.0000053.33333480.00000

Suppose that the manufacturing cost increases to $11.70per case for model A and the manufacturing cost for model B decreases to $4per unit. Would the optimal solution change?