Question: Gepbab Corporation produces three products at two different plants. The cost of producing a unit at each plant is shown in Table 6. Each plant can produce a total of 10,000 units. At least 6,000 units of product 1, at least 8,000 units of product 2, and at least 5,000 units of product 3 must be produced. To minimize the cost of meeting these demands, the following LP should be solved:

\(\min z=5 x_{11}+6 x_{12}+8 x_{13}+8 x_{21}+7 x_{22}+10 x_{23}\)

s.t. \(\quad x_{11}+x_{12}+x_{13} \quad \leq \quad 10,000\)

\(x_{21}+x_{22}+x_{23} \leq \quad 10,000\)

\(x_{11} \quad+x_{21} \quad \geq \quad 6,000\)

\(x_{12} \quad+x_{22} \quad \geq \quad 8,000\)

\(x_{13} \quad+x_{23} \geq \quad 5,000\)

All variables \(\geq \quad 0\)

Here, \(x_{i j}=\) number of units of product \(j\) produced at plant i. Use the LINDO output in Figure 9 to answer the following questions:

1. What would the cost of producing product 2 at plant 1 have to be for the firm to make this choice?
2. What would total cost be if plant 1 had 9,000 units of capacity?
3. If it cost $9 to produce a unit of product 3 at plant 1 , then what would be the new optimal solution?

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