$($Please show work and please show the optimal product mix that maximizes profit.$)$ Problem $310$ pts

A company manufactures two products, $x$ and $Y,$ using the same resources. Product $x$ has a contribution

margin of $$500$ per unit and a demand of $100$ units per month, while product $Y$ has a contribution margin of

$$750$ per unit and a demand of $60$ units per month. However, due to resource constraints, only $120$ units

$($ mix of $x$ and $Y)$ can be produced each month. Determine the optimal product mix that maximizes profit.