Use Excel to solve the linear programming problem.

At one of its factories, a manufacturer of televisions makes one or more of four models of HD units $($without cases$)$: a $20-$in$.$ LCD, a $42-$in$.$ LCD, a $42-$in$.$ plasma, and a $50-$in$.$ plasma. The assembly and testing time requirements for each model are shown in the table, together with the maximum amounts of time available per week for assembly and testing. In addition to these constraints, the supplier of cases indicated that it would supply no more than $210$ cases per week and that of these, no more than $40$ could be for the $20-$in$.$ LCD model.

Use the profit for each television shown in the table to find the number of completed models of each type that should be produced to obtain the maximum profit for the week. Find the maximum profit.

$20-$in$.$ LCD

sets

$42-$in$.$ LCD

sets

$42-$in$.$ plasma

sets

$50-$in$.$ plasma

sets

profit $

$20-$in$.$

LCD $42-$in$.$

LCD $42-$in$.$

Plasma $50-$in$.$

Plasma Total

Available

Assembly

time $($hours$)71012152000$

Test time

$($hours$)2245500$

Profit

$($dollars$)476075100$