Develop a mixed$-$integer programming model that could be used to help Martin$-$Beck determine which new plant or plants to open in order to satisfy anticipated demand. Solve the model and answer the following questions. What is the optimal cost?

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What is the optimal set of plants to open?

Kansas City

$($b$)$ Using equation $13\mathrm{.}1,$ find a second$-$best solution. What is the optimal set of plants to open?

Detroit & Denver

What is the increase in cost versus the best solution from part $($a$)?$