Chapter 11, Problem 94RE

To determine

Solve each linear programming problem.

Answer to Problem 94RE

  $\boxed{z=20at\left(2,4\right)}$

Explanation of Solution

Given information:

Solve each linear programming problem.

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

Calculation:

Consider the function.

  $z=2x+4y$

The graph of the feasible points is given as the value of $z$ is to be evaluated,

Now evaluate the given function $z=2x+4y$ , and tabulate as follows,

  $\begin{array}{cc}\begin{array}{l}CornerPo\mathrm{int}\\ \left(x,y\right)\end{array}& \begin{array}{l}ValueOfTheObjectiveFunction\\ z=2x+4y\end{array}\\ \left(2,0\right)& z=2\left(2\right)+4\left(0\right)=4\\ \left(2,4\right)& z=2\left(2\right)+4\left(4\right)=20\\ \left(6,0\right)& z=2\left(6\right)+4\left(0\right)=12\end{array}$

The maximum value of the objective function is $20$ at the coordinates $\left(2,4\right)$ .

Hence $\boxed{z=20at\left(2,4\right)}$ .