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 case for model B. Depending upon demand and the time available at the Newpark 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 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 as follows:

Min10AM+6BM+14AP+9BPs.t.1AM++1AP=100Demand for model A1BM+1BP=150Demand for model B4AM+3BM600Injection molding time6AM+8BM1,080Assembly timeAM,BM,AP,BP 0The sensitivity report is shown in the figure below.

Optimal Objective Value =2170.00000VariableValueReduced CostAM100.000000.00000BM60.000000.00000AP0.000001.75000BP90.000000.00000ConstraintSlack/SurplusDual Value10.0000012.2500020.000009.00000320.000000.0000040.00000-0.37500VariableObjective

CoefficientAllowable

IncreaseAllowable

DecreaseAM10.000001.75000InfiniteBM6.000003.000002.33333AP14.00000Infinite1.75000BP9.000002.333333.00000ConstraintRHS

ValueAllowable

IncreaseAllowable

1. Decrease1100.0000011.42857100.000002150.00000Infinite90.000003600.00000Infinite20.0000041080.0000053.33333480.00000Interpret the ranges of optimality for the objective function coefficients. If there is limit, then enter the text "NA" as your answer. If required, round your answers to two decimal place.
3. Ranges of OptimalityDecision Variablelower limitupper limitAMBMAPBP
5. Ifone
7. of the objective function coefficients is/are changed within the ranges above the optimal solutionwill not
9. change.
11. Suppose that the manufacturing cost increases to $11.20 per case for model A. If your answer is zero then enter "0".
13. Model VaraibleOptimal SolutionAMBMAPBP
14. Total Cost: $
16. Suppose that the manufacturing cost increases to $11.20 per case for model A and the manufacturing cost for model B decreases to $5 per unit. Would the optimal solution change? If your answer is zero then enter "0".
18. Yes
20. What is the new optimal solution?
21. Model VaraibleOptimal SolutionAMBMAPBP
22. Total Cost: $