Chapter 9.8, Problem 45E

To determine

To find the number of each type of beer that should be produced each day to maximize the profit.

Answer to Problem 45E

  $800$ Large beers and $400$ small beers.

Explanation of Solution

Given:

The company produces at least $300$ large stuffed and $400$ small stuffed beersper day and at most $1200$ bears per day. The profit for large bear is $\$9.00$ and the profit for small beersis $\$5.00$ .

Calculation:

Let $y$ be the number of large beersproduced and $x$ be the number of small beersproduced.

At any given day-

  $\begin{array}{l}x+y\le 1200\\ x\ge 400\\ y\ge 300\\ p(x,y)=9y+5x\end{array}$

The resultant graph will be a triangle which will have the following vertices- $(400,300),(900,300),(400,800)$ . Out of these the most profitable solution is $(400,800)$ with $\$9200$ profit.