and at most $\backslash (5\backslash \%\backslash )$ molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap steel, and alloys. Four steel ingots are available for purchase. The weight $($in tons$),$ cost per ton, carbon and molybdenum content of each ingot are given in the following table:

Once an ingot is purchased, any amount less than or equal to its weight can be used in the production of the steel. Three types of alloys can be purchased. The cost per ton and chemical makeup of each alloy are given in the following table:

Alloys can be purchased in any quantities. Steel scrap may be purchased $($in any quantity$)$ at a cost of $\backslash (\backslash$$ $100\backslash )$ per ton. Steel scrap contains $\backslash (2\backslash \%\backslash )$ carbon and $\backslash (8\backslash \%\backslash )$ molybdenum.

$($a$)(15$ points$)$ Formulate the company's problem as a mixed integer program to minimize the cost of filling the order. Define your decision variables clearly.

$($b$)(10$ points$)$ Solve the model you developed in part $($a$)$ using OpenSolver and report the optimal solution. Upload the excel file as well when uploading your solutions. $($Hint: Optimal objective function value is $\backslash (\backslash$$ $9768\mathrm{.}57\backslash ))$