Chapter 2.6, Problem 26E

To determine

To find: the maximum profit that can be expected in a day.

Answer to Problem 26E

$1080

Explanation of Solution

Given information:

Maximum tin of cookies production in a day = 200

Butter required for large tin of cookies = 2 pounds

Butter required for small tin of cookies = 1 pound

Maximum butter available in a day = 300 pounds.

Function for profit from cookies production is as follows:

  $f\left(x,y\right)=\$6.00x+\$4.80y$

Here x and y represents number of large tins sold and small tins sold respectively.

Calculation:

The inequalities derived from the given data are as follows:

  $\begin{array}{l}x+y\le 200\\ 2x+y\le 300\end{array}$

The graph for the inequalities is shown below.

  

The points satisfying both the inequalities are $\left(0,200\right),\left(100,100\right)$ and $\left(150,0\right)$ . Put the points in the function $f\left(x,y\right)$ to check the expected maximum profit of a day.

  $\begin{array}{c}f\left(0,200\right)=\$6.00\left(0\right)+\$4.80\left(200\right)\\ =0+\$960\\ =\$960\\ \\ f\left(100,100\right)=\$6.00\left(100\right)+\$4.80\left(100\right)\\ =\$600+\$480\\ =\$1080\\ \\ f\left(150,0\right)=\$6.00\left(150\right)+\$4.80\left(0\right)\\ =\$900+0\\ =\$900\end{array}$

Thus, the maximum profit that can be expected in a day is $1080.