Question

In problem 9-18,solve each linear programming problem.

Maximize $z=2x+4y$subject to$x\ge 0,y\ge 0,2x+y\ge 4,x+y\le 9$

Short answer

The maximum value of the objective function exists at the corner point given by the cordinates$(0,9)isz=36$

Step-by-step solution

Step 1. Given information

The given linear equation$z=2x+4y$

Step 2. Maximize the given linear equation

The graph of the feasible points is given at which the value of zis to be evaluated

Let us evaluate the objective function$z=2x+4y$at the feasible points given above and tabulate as follows:

Corner point(x,y)	Value of objection function $z=2x+4y$
$(0,4)$	localid="1647281488639" $z=2\left(0\right)+4\left(4\right)=16$
$(0,9)$	localid="1647281495096" $z=2\left(0\right)+4\left(9\right)=36$
localid="1647281514033" $(9,0)$	localid="1647281501556" $z=2\left(9\right)+4\left(0\right)=18$
localid="1647281519562" $(2,0)$	localid="1647281507482" $z=2\left(2\right)+4\left(0\right)=4$

The maximum value of the objective function exists at the corner point given by the cordinates (0,9) is$z=36$