Chapter 11, Problem 51RE

To determine

To find: The maximum value of objective function..

Answer to Problem 51RE

The maximum value of function is $32$ when $x=0,y=8$

Explanation of Solution

Given information:

Maximize $z=3x+4y$ subject to $x\ge 0,y\ge 0,3x+2y\ge 6$ .

Calculation:

Draw the graph of given inequalities and label the corners.

  

Figure-(1)

The corners and the corresponding values of objective functions are given below.

Corner Points $\left(x,y\right)$	Value of the objective function $z=3x+4y$
$\left(0,3\right)$	$\begin{array}{c}z=3\left(0\right)+4\left(3\right)\\ =12\end{array}$
$\left(0,8\right)$	$\begin{array}{c}z=3\left(0\right)+4\left(8\right)\\ =32\end{array}$
$\left(2,0\right)$	$\begin{array}{c}z=3\left(2\right)+4\left(0\right)\\ =6\end{array}$
$\left(8,0\right)$	$\begin{array}{c}z=3\left(8\right)+4\left(0\right)\\ =24\end{array}$

From the above table it is clear that the maximum value of objective function is $32$ and its corner points are $\left(0,8\right)$ .

Therefore, the maximum value of function is $32$ when $x=0,y=8$