(A) Find an Optimal Solution to the Problem

Question

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The Answer is (A)
SS = pounds of steel sheeting produced and sold = 1000
AS = pounds of aluminum sheeting produced and sold = 2000
SC = number of Standard chassis racks produced and sold = 800
DC = number of Deluxe chassis racks produced and sold = 1000
Profit = $26,200

(B)

(A) SS = pounds of steel sheeting produced and sold = 1000 AS = pounds of aluminum sheeting produced and sold = 2000 SC = number of Standard chassis racks produced and sold = 800 DC = number of Deluxe chassis racks produced and sold = 1000 Profit = $26,200 (B) Steel available, Aluminum available, Assembly SS, and Market Deluxe SS all have nonzero shadow prices, so they are binding. (C) Incremental contribution is $2 per hour, with an allowable increase of 25 hours. (D) The value of additional capacity on the polisher is zero, since it is not binding. The allowable increase is unbounded, and the allowable decrease is 1000. (E) The change in the profit would be $1.8/hour shadow price times 75 hours, or $135, so Western should adopt the plan. (F) Profit would increase by $8 (4 hours times $2/hour shadow price) (G) The optimal solution would not change, because the change in the objective coefficient is within the allowable decrease (-$0.8). Note that since this would not result in any more standard chassis being sold, profit would decrease by $400. (H) They should procure 1,000 pounds more of aluminum, since the shadow price is higher than that for steel (0.6 vs. 0.4). This results in additional profit of $600. (I) The total cost will be the sum of the repairs ($10,000), the outsourcing cost ($2.50 per chassis, extended by how many chassis will be produced) and any reduction in profit due to the restricted stamping capacity. Note that since the capacity reduction on stamping is greater than the allowable decrease, a new production plan will be required. This new plan (0 SS, 4,000 AS, 500 SC, 1,000 DC) results in profit of $23,400, which is a reduction of $2,800 from the existing optimal profit of $26,200. With the production plan determined, the outsourcing cost can be determined (500 SC + 1000 DC = 1500 * $2.50 = $3,750). Thus the total cost will be $10,000 + 2 months*($2,800 + $3,750) = $23,100.

Steel available, Aluminum available, Assembly SS, and Market Deluxe SS all have nonzero shadow prices, so they are binding.

(C) Incremental contribution is $2 per hour, with an allowable increase of 25 hours.

(D) The value of additional capacity on the polisher is zero, since it is not binding. The allowable increase is unbounded, and the allowable decrease is 1000.

(E) The change in the profit would be $1.8/hour shadow price times 75 hours, or $135, so Western should adopt the plan.

(F) Profit would increase by $8 (4 hours times $2/hour shadow price)

(G) The optimal solution would not change, because the change in the objective coefficient is within the allowable decrease (-$0.8). Note that since this would not result in any more standard chassis being sold, profit would decrease by $400.

(H) They should procure 1,000 pounds more of aluminum, since the shadow price is higher than that for steel (0.6 vs. 0.4). This results in additional profit of $600.

(I) The total cost will be the sum of the repairs ($10,000), the outsourcing cost ($2.50 per chassis, extended by how many chassis will be produced) and any reduction in profit due to the restricted stamping capacity. Note that since the capacity reduction on stamping is greater than the allowable decrease, a new production plan will be required. This new plan (0 SS, 4,000 AS, 500 SC, 1,000 DC) results in profit of $23,400, which is a reduction of $2,800 from the existing optimal profit of $26,200. With the production plan determined, the outsourcing cost can be determined (500 SC + 1000 DC = 1500 * $2.50 = $3,750). Thus the total cost will be $10,000 + 2 months*($2,800 + $3,750) = $23,100.

(A) Find an Optimal Solution to the Problem

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