Company Electrum produces electrical components, including a remote controller for TVs and a remote controller for VCRs$.$ Each controller consists of three subassemblies that are manufactured by Electrum; a base, a cartridge, and a keypad. Both controllers use the same base subassembly, but different cartridge and keypad subassemblies. Electrum$$s sales forecast indicates that $7000$ TV controllers and $5000$ VCR controllers will be needed to satisfy demand during the next planning period. Because only $500$ hours of in$-$house manufacturing time are available, Electrum is considering purchasing some, or all, of the units of each subassembly from outside suppliers. If Electrum manufactures a subassembly in$-$house, it incurs a fixed setup cost as well as a variable manufacturing cost. The table below shows the setup cost, the manufacturing time per unit of each subassembly, the manufacturing cost per unit of each subassembly, and the cost to purchase a unit of each subassembly from an outside supplier: Subassembly Setup cost $($$$)$ Manufacturing time per unit $($minutes$)$ Manufacturing cost per unit $($$$)$ Purchase cost per unit $($$$)$ Base $10000\mathrm{.}90\mathrm{.}400\mathrm{.}65$ TV cartridge $12002\mathrm{.}22\mathrm{.}903\mathrm{.}45$ VCR cartridge $19003\mathrm{.}03\mathrm{.}153\mathrm{.}70$ TV keypad $15000\mathrm{.}80\mathrm{.}300\mathrm{.}50$ VCR keypad $15001\mathrm{.}00\mathrm{.}550\mathrm{.}70$ a$)$ Develop an optimization model to determine how many units of each subassembly Electrum should manufacture and how many units of each subassembly Electrum should purchase to minimize the total cost of satisfying the demand. Solve it using Excel solver, state your recommendation, and put screenshots of the supporting computer outputs in the appendix. What is the total cost $($setup$,$ manufacturing, and purchase$)$ associated with your recommendation?