Chapter 11: Q. 11 (page 790)

Solve each linear programming problem.
Minimize $2 x + 5 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x \leq 5 \\ y \leq 3 \end{cases}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

The given system of linear inequalities is :

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x \leq 5 \\ y \leq 3 \end{cases}$

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)	$z = 2 x + 5 y$
$(0, 2)$	$z = 10$
$(0, 3)$	$z = 15$
$(2, 0)$	$z = 4$
$(5, 0)$	$z = 10$
$(5, 3)$	$z = 25$

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Solve each linear programming problem.
Minimize $2 x + 5 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x \leq 5 \\ y \leq 3 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

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Solve each linear programming problem.Minimize 2x+5ysubject to x≥0y≥0x+y≥2x≤5y≤3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Draw the graph of the system

Step 3. Make a table for the corner points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Solve each linear programming problem.
Minimize $2 x + 5 y$ subject to $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x \leq 5 \\ y \leq 3 \end{cases}$