Machine $1$ is available for $150$ hours, machine $2$ for $240$ hours, machine $3$ for $200$ hours,

and machine $4$ for $250$ hours. The products also result in different profits, according to the

machine they are produced on$,$ because of time, waste, and operating cost. The profit per

unit per machine for each product is summarized as follows:

The company wants to know how many units of each product to produce on each machine

to maximize profit.

$($a$)$ Formulate a linear programming model for this problem.

$($b$)$ Solve the model by using excel solver