Problem $3$

The Midland Tool Shop has four heavy presses it uses to stamp out prefabricated

Metal covers and housings for electronic consumer products.

All four presses operate differently and are of different sizes. Currently the firm has a

contract to produce three products. The contract calls for $400$ units of product $1,570$

units of product $2,$ and $320$ units of product

$3.$ The time $($in minutes$)$ required for each product to be produced on each machine is as

follows

Machine

Product $1234$

$135413439$

$240363243$

$338373340$

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:

Machine

Product $1234$

$17\mathrm{.}87\mathrm{.}88\mathrm{.}27\mathrm{.}9$

$26\mathrm{.}78\mathrm{.}99\mathrm{.}26\mathrm{.}3$

$38\mathrm{.}48\mathrm{.}19\mathrm{.}05\mathrm{.}8$

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 the Excel Solver.