Q35. - Algebra 2

Question

35  Wood pulp can be converted to either notebook paper or newsprint. The Canyon Pulp and Paper Mill can produce at most$200$ units of paper a day.egular customers require at least 10 units of notebook paper and$80$ units of newspaper daily. If the profit on a unit of notebook paper is \(500 and the profit on a unit of newsprint is \)$350$, how many units of each type of paper should the mill produce each day to maximize profits? 

Step-by-Step Solution

Answer

The maximum profit is $$88000$ when Mill more$120$ notebook paper no $80$ newsprint.

Step-1 – Define the variables

$x=$Number of notebook paper.

$y=$Number of newsprint.

Step-2 – Write system of inequalities

Since the number of paper cannot be negative. $x$and$y$ must be nonnegative numbers.

$x\ge 0,y\ge 0.$

The canyon pulp and paper Mill can produce at most 200 notebooks.

$x+y\le 200.$

Regular customer requires at least$10$ units of notebook and$80$units of newsprint.

$x\le 10$ and$y\le 80$

Step-3 – Graph the system of inequalities

Step-4 –Find the co-ordinate of the vertices of the feasible region

From the graph, the vertices of the feasible region are at$\left(10,80\right)$, $\left(10,190\right)$ and$(120,80)$

Step-5 –Write the function to be maximized or minimized

The function that describe the maximum profit is

$f\left(x,y\right)=500x+350y$

Step-6 –Substitute the co-ordinate of the vertices into the function.

Step-7 –Select the greatest result

The maximum value of the function is$88000\left(180,60\right)$.This means that the maximum profit is $$88000$ when Mill makes$120$-notepaper and$80$ newsprint