Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

Solve each linear programming problem.

Minimize $2x+5y$ subject to $\left\{\begin{array}{l}x\ge 0\\ y\ge 0\\ x+y\ge 2\\ x\le 5\\ y\le 3\end{array}\right.$

Step-by-Step Solution

Answer

The minimum value is at $4$. We get this value at point $(2,0)$

Step 1. Given information

The given system of linear inequalities is :

$\left\{\begin{array}{l}x\ge 0\\ y\ge 0\\ x+y\ge 2\\ x\le 5\\ y\le 3\end{array}\right.$

The goal of the task is to solve the problem of linear programming. We are looking for the smallest 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)	$z=2x+5y$
$(0,2)$	$z=10$
$(0,3)$	$z=15$
$(2,0)$	$z=4$
$(5,0)$	$z=10$
$(5,3)$	$z=25$