Chapter 11.7, Problem 58AYU

Manufacturing Trucks Mike’s Toy Truck Company manufactures two models of toy trucks, a standard model and a deluxe model. Each standard model requires 2 hours (h) for painting and 3 h for detail work; each deluxe model requires 3 h for painting and 4 h for detail work. Two painters and three detail workers are employed by the company, and each works 40 h per week.

a. Using $x$ to denote the number of standard-model trucks and $y$ to denote the number of deluxe-model trucks, write a system of linear inequalities that describes the possible numbers of each model of truck that can be manufactured in a week.

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 each model of truck that can be manufactured in a week.

2. To graph the system and label the corner points.

Answer to Problem 58AYU

Solution:

$x \ge 0, y \ge 0, 2x + 3y \le 80, 3x + 4y \le 120$

Explanation of Solution

Given:

	Painting	Detail work
Standard model	2h	3h
Deluxe model	3h	4h

2 painters and 3 detail workers are employed by the company and each works 40 h/week.

Calculation:

Begin by assigning symbols for the two variables.

$x = \text{Number of standard model trucks}.$

$y = \text{Number of deluxe model trucks}.$

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

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

From the given data we get

$2x + 3y \le 80$

$3x + 4y \le 120$

1. Therefore, a system of linear inequalities that describes the possible numbers of each model of truck that can be manufactured in a week.

$x \ge 0$

$y \ge 0$

$2x + 3y \le 80$

$3x + 4y \le 120$

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