Chapter 8, Problem 60RE

(a)

To determine

The objective function modelling the profit on daily basis in context with a manufacturing company which makes the conversion of wood pulps into the writing paper. Profit earned is $500 per unit on the writing paper and $350 on the news print.

(b)

To determine

The system of 3 inequalities which models the constraints that factory’s equipment allows for producing maximum $200$ units of paper per day. Regular customers need minimum $10$ units of writing paper and $80$ units of newsprint daily.

(c)

To determine

To graph: The inequalities $\begin{array}{l}x+y\le 200\\ x\ge 10\\ y\ge 80\end{array}$ in quadrant I only as x and y must be positive.

(d)

To determine

To calculate: The value of the objective function $z=500x+350y$ at three vertices $\left(10,80\right),\left(10,190\right),\left(120,80\right)$ of graphed region.

(e)

To determine

To fill: The blank spaces in the given statement, “The company will make the greatest profit by producing __________ units of writing paper and ___________ units of newsprint each day. The maximum daily profit is $___________. ”