Examine Problem $12$ on Page $101.$ Problem $12$ is about the "United Aluminum Company of Cincinnati". Formulate a linear programming model for it$.$ After you formulate the model, solve it using Excel Solver like you learned in class. Make sure you ask Solver to give you the sensitivity report. Based on the report, answer the following questions:

A$.$ Interpret the meaning of the three shadow prices in the sensitivity report. Your answer must be thorough.

B$.$ Which constraints are binding? Which constraints are non$-$binding?

C$.$ The manufacturing firm has contacted United Aluminum to inform them of their intention to reduce the size of the contract for medium$-$grade aluminum from $8$ tons to $6\mathrm{.}5.$ What impact will that have on United's cost? Explain using numbers.

D$.$ Would the solution value change if the contract requirements for high$-$grade aluminum were increased from $12$ tons to $20$ tons? Explain your answer. Yes or No is not enough.

Part II