b) (20 points) Suppose that the company can reduce the unit times on operations 1,2, and 3 for toy trains from the current levels of 1, 3, and 1 minute to 0.5, 1, and 0.5 minutes respectively. The revenue per unit is changed to $4. Determine the new optimal solution.

c) (20 points) Suppose that a new toy (fire engine) requires 3, 2, and 4 minutes, respectively, on operations 1, 2, and 3. Determine the optimal solution if the revenue per unit is $10.

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TOYCO assembles three types of toys -trains, trucks, and cars -using three operations. Available assembly times for the three operations are 430, 460, and 420 minutes per day respectively, and the revenues per toy train, truck, and car are $3, $2, and $5, respectively. The assembly times per train for the three operations are 1, 3, and 1 minutes, respectively. The corresponding times per truck and per car are (2, 0, 4) and (1, 2, 0) minutes (a zero time indicates that the operation is not used). Letting X₁, X2 and x3 represent the daily number of units assembled of trains, trucks, and cars, the optimal tableau is given as: BV Z X₂ X6 X3 X1 4 -1/4 3/2 2 X2 0 1 0 0 X3 0 0 1 0 Cors X4 1 1/2 0 -2 X5 2 -1/4 1/2 1 X6 0 0 0 1 RHS 1350 100 230 20 e a) (20 points) Toy trains are not part of the optimal production mix. The company recognizes that market competition will not allow raising the unit price of the toy. Instead, the company wants to concentrate on improving the assembly operation itself. This entails reducing the assembly time per unit in each of the three operations by a specified percentage, p%. Determine the value of p that will make toy trains just profitable. TOYCO assembles three types of toys -trains, trucks, and cars -using three operations. Available assembly times for the three operations are 430, 460, and 420 minutes per day respectively, and the revenues per toy train, truck, and car are $3, $2, and $5, respectively. The assembly times per train for the three operations are 1, 3, and 1 minutes, respectively. The corresponding times per truck and per car are (2, 0, 4) and (1, 2, 0) minutes (a zero time indicates that the operation is not used). Letting X₁, X2 and x3 represent the daily number of units assembled of trains, trucks, and cars, the optimal tableau is given as: BV Z X₂ X6 X3 X1 4 -1/4 3/2 2 X2 0 1 0 0 X3 0 0 1 0 Cors X4 1 1/2 0 -2 X5 2 -1/4 1/2 1 X6 0 0 0 1 RHS 1350 100 230 20 e a) (20 points) Toy trains are not part of the optimal production mix. The company recognizes that market competition will not allow raising the unit price of the toy. Instead, the company wants to concentrate on improving the assembly operation itself. This entails reducing the assembly time per unit in each of the three operations by a specified percentage, p%. Determine the value of p that will make toy trains just profitable.

Answer rating: 100% (QA)

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