Question

1. XYZ can manufacture three products. Each product consists totally of raw material 1 and raw material 2. The compositions of each product and the profit earned from each product are shown in the table below. Fifty board feet of raw material 1 and 100 kg of raw material 2 are available. After defining x_i to be the number of product i manufactured, XYZ should solve the following LP: Product | Raw material 1 | Raw material 2 | Profit (Cents) 1 | 1 | 2 | 3 2 | 1 | 3 | 7 3 | 1 | 1 | 5 max z = 3x_1 + 7x_2 + 5x_3 s.t. x_1 + x_2 + x_3 ? 50 2x_1 + 3x_2 + x_3 ? 100 x_1, x_2, x_3 ? 0 After adding slack variables s_1 and s_2, the optimal tableau is as shown in the next table. Using this optimal tableau, answer the following questions: z | x_1 | x_2 | x_3 | s_1 | s_2 | RHS 1 | 3 | 0 | 0 | 4 | 1 | 300 0 | 1/2 | 0 | 1 | 3/2 | -1/2 | 25 0 | 1/2 | 1 | 0 | -1/2 | 1/2 | 25 a) For what values of Product 1 profit, does the current basis remain optimal? If the profit for a Product 1 were 7¢, what would be the new optimal solution to XYZ's problem? (20 points) b) If 60 board feet of raw material 1 were available, what would be XYZ's profit? How many of each product should the company make? (20 points)

          1. XYZ can manufacture three products. Each product consists totally of raw material 1 and raw material 2. The compositions of each product and the profit earned from each product are shown in the table below. Fifty board feet of raw material 1 and 100 kg of raw material 2 are available. After defining x_i to be the number of product i manufactured, XYZ should solve the following LP:

Product | Raw material 1 | Raw material 2 | Profit (Cents)
1 | 1 | 2 | 3
2 | 1 | 3 | 7
3 | 1 | 1 | 5

max z = 3x_1 + 7x_2 + 5x_3
s.t. x_1 + x_2 + x_3 ? 50
2x_1 + 3x_2 + x_3 ? 100
x_1, x_2, x_3 ? 0

After adding slack variables s_1 and s_2, the optimal tableau is as shown in the next table. Using this optimal tableau, answer the following questions:

z | x_1 | x_2 | x_3 | s_1 | s_2 | RHS
1 | 3 | 0 | 0 | 4 | 1 | 300
0 | 1/2 | 0 | 1 | 3/2 | -1/2 | 25
0 | 1/2 | 1 | 0 | -1/2 | 1/2 | 25

a) For what values of Product 1 profit, does the current basis remain optimal? If the profit for a Product 1 were 7¢, what would be the new optimal solution to XYZ's problem? (20 points)
b) If 60 board feet of raw material 1 were available, what would be XYZ's profit? How many of each product should the company make? (20 points)

1. XYZ can manufacture three products. Each product consists totally of raw material 1 and raw material 2. The compositions of each product and the profit earned from each product are shown in the table below. Fifty board feet of raw material 1 and 100 kg of raw material 2 are available. After defining xi to be the number of product i manufactured, XYZ should solve the following LP:

Product | Raw material 1 | Raw material 2 | Profit (Cents)
1 | 1 | 2 | 3
2 | 1 | 3 | 7
3 | 1 | 1 | 5

max z = 3x1 + 7x2 + 5x3
s.t. x1 + x2 + x3 ? 50
2x1 + 3x2 + x3 ? 100
x1, x2, x3 ? 0

After adding slack variables s1 and s2, the optimal tableau is as shown in the next table. Using this optimal tableau, answer the following questions:

z | x1 | x2 | x3 | s1 | s2 | RHS
1 | 3 | 0 | 0 | 4 | 1 | 300
0 | 1/2 | 0 | 1 | 3/2 | -1/2 | 25
0 | 1/2 | 1 | 0 | -1/2 | 1/2 | 25

a) For what values of Product 1 profit, does the current basis remain optimal? If the profit for a Product 1 were 7¢, what would be the new optimal solution to XYZ's problem? (20 points)
b) If 60 board feet of raw material 1 were available, what would be XYZ's profit? How many of each product should the company make? (20 points)

Added by Kristen C.

Question

Please give Ace some feedback