Solution to P2 Sensitivity at the Major Electric Company

Transcription

1 Solution to P2 Sensitivity at the Major Electric Company 1.(a) Are there alternate optimal solutions? Yes or no. (b) If yes, which nonbasic variables could enter the basis without changing the value of the objective function? 2. (a) Which of the washing machines can have their unit profits increase unbounded without changing the production levels? (b) Which of the clothes dryers can have their unit profits decrease unbounded without changing the production levels? 3. (a) What would be the increase in profit if the unit profit of product 17 were increased by $20? (b) What would be the decrease in profit if the unit profit of product 20 were decreased by $10? 4. (a) What would be the new unit profit coefficient if the unit profit of product 32 were increased to its allowable value? (b) What would be the new 6-month profit if this change occurred? 5. (a) What would be the new unit profit coefficient if the unit profit of product 24 were decreased to its allowable value? (b) What would be the new maximum total 6-month profit if this change occurred? 6. Over what range can the production cost budget of $1,750,000 change without requiring a new basic solution? (b) What would be the resulting loss in profit if the budget were to be decreased by $100,000? 7. (a) If additional hours can be added to one of the manufacturing cells, which one would increase the profit at the greatest rate without requiring a change of basis solution? (b) What would be the increase in profit if the hours of this cell were increased to allowable maximum? 8. (a) Which manufacturing cells if any have unused available hours? (b) If cell C were to lose 150 hours, what would be the effect on the profit? 9. (a) Which product will increase the profit at the greatest rate as the upper bound increases? (b) What is the increase in profit if the upper bound is increased to its allowable maximum? 10. (a) Considering both the rate of increase in profit as the upper bound increases as well as the allowable increase in the upper bound, which product will generate the largest increase in profit if it s at its maximum increase? (b) What would be the resulting profit?

2 Question Response (a) Response (b) 1. Yes 3, 5, 9, 10, 25, Prod 17: 20 x 105 = $2100 Prod 20: 10 x 100 = $1,000 4.prod = $ Profit = $ 273,724 + (52) (33.175) = $ 273, = $275, prod = Budget can increase unbounded and decrease by $346, Profit = $ 273,724 - (75) (46.766) = $ 273, = $270, cell A profit would increase by for each additional hour None Product 14 Product 30 Increase = (26.512)(419.5) = $11, new profit = $ 273, , = 284, Decrease = (150)( ) = New profit = $ 273, = 271, x = 13, Profit = 287, (89.619) ( ) = 37, Profit = 311, Each response is worth 5 points.

3 Sensitivity Report Final Reduced Objective Allowable Allowable product Name Value Cost Coefficient Increase Decrease 1 A changing cells E+30 2 A changing cells E+30 3 A changing cells E+30 4 A changing cells E+30 5 A changing cells E+30 6 A changing cells E A changing cells A changing cells E+30 9 A changing cells E B changing cells E B changing cells E B changing cells B changing cells E B changing cells E B changing cells E C changing cells E C changing cells E C changing cells E C changing cells E C changing cells E C changing cells C changing cells E C changing cells E C changing cells E C changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells E D changing cells D changing cells E D changing cells E

4 Final Shadow Constraint Allowable Allowable product Name Value Price R.H. Side Increase Decrease 1 upper bnd E A upper bnd E A upper bnd E A upper bnd E A upper bnd -3.55E E A upper bnd A upper bnd E A upper bnd E A upper bnd E B upper bnd E B upper bnd B upper bnd E B upper bnd B upper bnd B upper bnd C upper bnd E C upper bnd C upper bnd C upper bnd C upper bnd C upper bnd E C upper bnd C upper bnd E C upper bnd C upper bnd E D upper bnd E D upper bnd D upper bnd D upper bnd D upper bnd D upper bnd D upper bnd E D upper bnd D upper bnd E D upper bnd E D upper bnd D upper bnd A lower bnd A lower bnd A lower bnd A lower bnd A lower bnd A lower bnd E+30 7 A lower bnd E+30 8 A lower bnd A lower bnd

5 Final Shadow Constraint Allowable Allowable product Name Value Price R.H. Side Increase Decrease 10 B lower bnd B lower bnd E B lower bnd E B lower bnd E B lower bnd E B lower bnd E C lower bnd C lower bnd E C lower bnd E C lower bnd E C lower bnd E C lower bnd E C lower bnd E C lower bnd C lower bnd E C lower bnd D lower bnd D lower bnd E D lower bnd E D lower bnd E D lower bnd E D lower bnd E D lower bnd D lower bnd E D lower bnd D lower bnd E D lower bnd E D lower bnd E+30 total units t E cell A cell hrs cell B cell hrs cell C cell hrs cell D cell hrs Assembly Hours per unit E Finishing hours per unit E Inspection Hours per unit E prod cost $1,403, E