$(6$ Points$)$ Linear Programming:

A small factory produces two products, $x$ and $Y.$ The profit per unit is $$30$ for

$x$ and $$50$ for $Y.$ The factory has the following constraints:

Production time: $4x+5Y200$ hours

Materials: $3x+2Y150$ units

$x,Y0$

a$)$ Formulate the Linear Programming model to maximize profit.

b$)$ Solve graphically to determine the optimal production levels.