Question

Solve each linear programming problem.

Maximize$z=2x+y$subject to$\left\{\begin{array}{l}x\ge 0\\ y\ge 0\\ x+y\le 6\\ x+y\ge 1\end{array}\right.$

Short answer

Maximum value is $12$, we get this value at$(6,0)$

Step-by-step solution

Step 1. Given information

The given system of linear inequalities is :

$\left\{\begin{array}{l}x\ge 0\\ y\ge 0\\ x+y\le 6\\ x+y\ge 1\end{array}\right.$

The goal of the task is to solve the problem of linear programming. We are looking for the largest value that can occur if x and y are solutions of the system. We draw a graph of the system and read the corner points from the graph.

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

Corner point (x,y)	$z=2x+y$
$(0,1)$	role="math" localid="1646997454100" $z=1$
$(0,6)$	$z=6$
$(6,0)$	$z=12$
$(1,0)$	$z=2$