Concept explainers
Cost Function The simplest cost function is the linear cost function, , where the represents the fixed costs of operating a business and the slope represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of , and each bicycle costs to manufacture.
a. Write a linear model that expresses the cost of manufacturing bicycles in a day.
b. Graph the model.
c. What is the cost of manufacturing 14 bicycles in a day?
d. How many bicycles could be manufactured for ?
To calculate:
a. Write a linear model that expresses the cost of manufacturing bicycles in a day.
b. Graph the model.
c. What is the cost of manufacturing 14 bicycles in a day?
d. How many bicycles can be manufactured for ?
Answer to Problem 47AYU
Solution:
a.
b. The cost of manufacturing 14 bicycles in a day is .
c. The graph is as shown below:
d. 22 bicycles can be manufactured from .
Explanation of Solution
Given:
The bicycle manufacturer has daily fixed costs of , and each bicycle costs to manufacture.
Formula used:
A linear equation is of the form , where is the average rate if change of that function and is the , which is the initial value of the function when .
a.
The linear model that expresses the cost of manufacturing bicycles in a day is .
b.
The graph of the linear function is
c.
When , we get
The cost of manufacturing 14 bicycles in a day is .
d.
When , we get
Therefore, 22 bicycles can be manufactured from .
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