   Chapter 1, Problem 22RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and$12,000 to produce 1500 toaster ovens a week. (a) Express the cost as a function of the number of toaster ovens produced, assuming that it is linear. Then sketch the graph. (b) What is the slope or the graph and what does it represent? (c) What is the y-intercept of the graph and what does it represent?

(a)

To determine

To express: The cost as a function of the number of toaster ovens produced.

Explanation

Given:

To produce 1000 toaster ovens in a week it costs $9000 and to produce 1500 it costs$12000.

The cost function follows a liner function.

Calculation:

Let the cost function as, yy1=m(xx1). (1)

The slope of the line m is given by m=yy1xx1.

According to the given data, there exist two points (1000,9000) and (1500,12000).

The slope of line passes through (1000,9000) and (1500,12000) is,

m=12000900015001000=6

Substitute m=6 in equation (1)

(b)

To determine

To find: The slope of graph and explain what it represent.

(c)

To determine

To find: The y-intercept of graph and explain what it represent.

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