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 Min10 AM 6 BM 14 AP 9 BP s t 1 AM 1 AP 100Demand for model A1 BM 1 BP 150Demand for model B4 AM 3 BM 600Injection molding time6 AM 8 BM 1,080Assembly time AM , BM , AP , BP 0The sensitivity report is shown in the figure below Optimal Objective Value 2170 00000VariableValueReduced Cost AM 100 000000 00000 BM 60 000000 00000 AP 0 000001 75000 BP 90 000000 00000ConstraintSlack SurplusDual Value10 0000012 2500020 000009 00000320 000000 0000040 00000 0 37500VariableObjective CoefficientAllowable IncreaseAllowable Decrease AM 10 000001 75000Infinite BM 6 000003 000002 33333 AP 14 00000Infinite1 75000 BP 9 000002 333333 00000ConstraintRHS ValueAllowable IncreaseAllowable 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 Ranges of OptimalityDecision Variablelower limitupper limit AMBMAPBP If one of the objective function coefficients is are changed within the ranges above the optimal solution will not change Suppose that the manufacturing cost increases to $11 20 per case for model A If your answer is zero then enter 0 Model VaraibleOptimal Solution AMBMAPBP Total Cost $ 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 Yes What is the new optimal solution Model VaraibleOptimal Solution AMBMAPBP Total Cost $

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 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  Min10 AM  6 BM  14 AP  9 BP s t 1 AM   1 AP  100Demand for model A1 BM  1 BP  150Demand for model B4 AM  3 BM 600Injection molding time6 AM  8 BM 1,080Assembly time AM , BM , AP , BP 0The sensitivity report is shown in the figure below  Optimal Objective Value  2170 00000VariableValueReduced Cost AM 100 000000 00000 BM 60 000000 00000 AP 0 000001 75000 BP 90 000000 00000ConstraintSlack SurplusDual Value10 0000012 2500020 000009 00000320 000000 0000040 00000 0 37500VariableObjective CoefficientAllowable IncreaseAllowable Decrease AM 10 000001 75000Infinite BM 6 000003 000002 33333 AP 14 00000Infinite1 75000 BP 9 000002 333333 00000ConstraintRHS ValueAllowable IncreaseAllowable 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  Ranges of OptimalityDecision Variablelower limitupper limit AMBMAPBP If one of the objective function coefficients is are changed within the ranges above the optimal solution will not change  Suppose that the manufacturing cost increases to $11 20 per case for model A  If your answer is zero then enter  0   Model VaraibleOptimal Solution AMBMAPBP Total Cost  $ 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   Yes What is the new optimal solution  Model VaraibleOptimal Solution AMBMAPBP Total Cost  $

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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

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