Problem $1(30$ points$)$

Formulate a Linear Programming model to identify the optimum production quantity, so the company maximizes its profit. An appliance manufacturer produces two models of microwave ovens: H and $\backslash ($ W $\backslash ).$ Both models require fabrication and assembly work; each $\backslash ($ H $\backslash )$ uses four hours of fabrication and two hours of assembly, and each $\backslash ($ W $\backslash )$ uses two hours of fabrication and six hours of assembly. There are $600$ fabrication hours available this week and $480$ hours of assembly.

Each $\backslash ($ H $\backslash )$ contributes $\backslash (\backslash$$ $40\backslash )$ to profits, and each $\backslash ($ W $\backslash )$ contributes $\backslash (\backslash$$ $30\backslash )$ to profits. What quantities of $\backslash ($ H $\backslash )$ and $\backslash ($ W $\backslash )$ will maximize profit? Use the Graphical LP and enumeration methods to find the optimum solution. $[$Hint: You can use Excel to confirm you got the correct solution.$]$