Chapter 11.7, Problem 61AYU

Transporting Goods A small truck can carry no more than 1600 pounds (lb) of cargo and no more than 150 cubic feet $\left(f{t}^3\right)$ of cargo. A printer weighs 20 lb and occupies $3f{t}^3$ of space. A microwave oven weighs 30 lb and occupies $2f{t}^3$ of space.

a. Using $x$ to represent the number of microwave ovens and $y$ to represent the number of printers, write a system of linear inequalities that describes the number of ovens and printers that can be hauled by the truck.

b. Graph the system and label the corner points.

To determine

To find:

1. To write a system of linear inequalities that describes the possible numbers of ovens and printers that can be hauled by the truck.

2. To graph the system and label the corner points

Answer to Problem 61AYU

Solution:

$x \ge 0, y \ge 0, 3x + 2y \le 160, 2x + 3y \le 150$

Explanation of Solution

Given:

	Weighs	Space occupies
Microwave oven	$30lb$	2 ft3
Printers	$20lb$	3 ft3

Truck can carry no more than $1600lb$ of cargo and no more than 150 ft³ of cargo.

Calculation:

Begin by assigning symbols for the two variables.

$x = \text{Number of microwave ovens}.$

$y = \text{Number of printers}.$

Because $x$ and $y$ represents the number of items, the only meaningful values of $x$ and $y$ are non–negative.

Therefore, $x \ge 0, y \ge 0$

From the given data we get,

$30x + 20y \le 1600 => 3x + 2y \le 160$

$2x + 3y \le 150$

Therefore, a system of linear inequalities that describes the possible amounts of each investment are

$x \ge 0$

$y \ge 0$

$3x + 2y \le 160$

$2x + 3y \le 150$

2. The graph of the system and corner points are illustrated in the figure below.