Chapter 4.5, Problem 16ES

(a)

To determine

The objective function to model the total monthly profit, if The profit per unit is $125 for rear projection television and $200 for the plasma television

(b)

To determine

The system of three inequalities that model the constraints.

(a) Equipment in the factory allows for making at most $450$ rear projection televisions in one month.

(b) Equipment in the factory allows for making at most $200$ plasma televisions in one month.

(c) The cost to the manufacturer per unit is $\$600$ for the rear projection televisions and $\$900$ for the plasma televisions. Total monthly costs cannot exceed $\$360,000$.

(c)

To determine

To graph: Graph the system of inequalities in part (b).

$\begin{array}{l}x\le 450\\ y\le 200\\ 600x+900y\le 360,000\end{array}$

(d)

To determine

The total monthly profit at each of the five vertices of the graphed region in (c).

(e)

To determine

To fill: The blanks of the statement “The blanks of the statement “The television manufacturer will make the greatest profit by manufacturing ____ rear-projection television each month and ____ plasma television each month. The maximum monthly profit is $_____.”