Question

AN=UNITS OF MODEL A PRODUCED ON THE NEW PRODUCTION LINE

AO= UNITS OF MODEL A PRODUCED ON THE OLD PRODUCTION LINE

BN= UNITS OF MODEL B PRODUCED ON THE NEW PRODUCTION LINE

BO= UNITS OF MODEL B PRODUCED ON THE OLD PRODUCTION LINE

MIN 30AN+50AO+25BN+40BO=Z

SUBJECT TO,                                                                                                    

AN+AO ≥ 50,000 Minimum production of model A

BN+BO ≥ 70,000 Minimum production of model B

AN+BN ≤ 80,000 Capacity of new production line

AO+BO ≤ 60,000 Capacity of old production line

OBJECTIVE FUNCTION VALUE

        1)      3850000.

VARIABLE        VALUE              REDUCED COST

        AN               50000.000000          0.000000

        AO                       0.000000          5.000000

        BN               30000.000000          0.000000

        BO              40000.000000            0.000000

       Constraints   SLACK OR SURPLUS     DUAL PRICES

        1)                          0.000000                      45.000000

        2)                          0.000000                       40.000000

        3)                          0.000000                      -15.000000

        4)                           20000.000                      0.000000

                         

VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE

                                 COEF                 INCREASE           DECREASE

       AN                   30.000000         5.000000                  INFINITY

       AO                   50.000000         INFINITY                5.000000

       BN                   25.000000          15.000000                 5.000000

       BO                   40.000000           5.000000                15.000000                   

      Constraints         CURRENT        ALLOWABLE        ALLOWABLE

                                    RHS                 INCREASE             DECREASE

          1                    50000.000000     20000.000000           40000.000000

          2                    70000.000000     20000.000000           40000.000000

          3                    80000.000000     40000.000000           20000.000000

          4                    60000.000000         INFINITY             20000.000000

                2 Points each

1. Would you recommend increase or decrease the capacity of the old production line? Why?
2. The production cost for model A on the old production is $50 per unit. How much would

this cost have to change to make it worthwhile to produce A on the old production line? Explain.

3. Suppose that the minimum production requirement for model B is reduced from 70,000 units to 60,000 units. What effect would this change have on optimal solution and the total production cost? Explain.
4. If capacity of new production line increase from 80,000 to 90,000 then what effect it will have on Total production cost? What will be the new total production cost?
5. Suppose that the production cost for model B on the new production line increases from $25 to $35 and the production cost for model B on the old production line decreases from $40 to $32. Would the optimal solution change?

P/S : Do Not Use Microsoft EXCEL to explain the answers. Please show and explain the answers in WORDS.

Answer 1

A. Would you recommend increase or decrease the capacity of the old production line? Why?

Answer: Decrease of the capacity of old production line is recommended as there is slack of 20000 which can be reduced from the existing capacity of old production line

B.The production cost for model A on the old production is $50 per unit. How much would this cost have to change to make it worthwhile to produce A on the old production line? Explain.

Answer: Reduced cost of Model A is 5 on the old production which means cost needs to be change to 50-5 = 45 to make it worthwhile to produce A on the old production line

C.Suppose that the minimum production requirement for model B is reduced from 70,000 units to 60,000 units. What effect would this change have on optimal solution and the total production cost? Explain.

Minimum requirement for model B has shadow price of 40 which is valid for reduction of 40000 units. hence reduction of minimum requirement by 10000 units will reduce total production cost by 40*10000 = 400000 and optimal solution will be AN = 50000,AO=0,BN=30000,BO = 30000 as cost is higher for BO than BN, reduced amount of production will be adjusted from BO

D. If capacity of new production line increase from 80,000 to 90,000 then what effect it will have on Total production cost? What will be the new total production cost?

new production line constraint has shadow price of -15 which is valid for increase of another 20000 units hence increase by 10000 units (80000 to 90000) will reduce cost by 10000*15= 150000

New total production cost = 3850000-150000 = 3700000

E.Suppose that the production cost for model B on the new production line increases from $25 to $35 and the production cost for model B on the old production line decreases from $40 to $32. Would the optimal solution change?

Yes. Optimal solution would change as although the increase in BN and decrease in BO are within their respective allowable increase and decrease range, changing both decision variable simultaneously do not hold true range of optimality theory