Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

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 z is 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 $z=2x+4y$
$(0,4)$	$z=2\left(0\right)+4\left(4\right)=16$
$(0,9)$	$z=2\left(0\right)+4\left(9\right)=36$
$(9,0)$	$z=2\left(9\right)+4\left(0\right)=18$
$(2,0)$	$z=2\left(2\right)+4\left(0\right)=4$

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