Concept explainers
a.
To write:
A function for your total costs,
a.
Answer to Problem 29E
The function for total costs would be
Explanation of Solution
Given:
You make and sell birdhouses. Your fixed cost for your tools and workspace are $3000. The cost of wood and other materials needed to make a birdhouse is $10. You sell each birdhouse for $50.
Calculation:
Let x represent the number of birdhouses make and sell.
We have been given that cost of wood and other materials needed to make a birdhouse is $10, so cost of materials for x birdhouses would be 10x .
The total cost of making x birdhouses would be cost of materials plus fixed costs (3000).
Therefore, thefunction for total costs would be
b.
To write:
A function for your total income,
b.
Answer to Problem 29E
The function for total income would be
Explanation of Solution
Given:
You make and sell birdhouses. Your fixed cost for your tools and workspace are $3000. The cost of wood and other materials needed to make a birdhouse is $10. You sell each birdhouse for $50.
Calculation:
Let x represent the number of birdhouses make and sell.
We have been given that yousell each birdhouse for $50, so income from sellingx birdhouses would be 50x .
Therefore, thefunction for income would be
c.
To write:
A function for your profit,
c.
Answer to Problem 29E
The function for profit would be
Explanation of Solution
Given:
You make and sell birdhouses. Your fixed cost for your tools and workspace are $3000. The cost of wood and other materials needed to make a birdhouse is $10. You sell each birdhouse for $50.
Calculation:
We know that profit is difference of income and total costs.
To write the profit function, we will subtract cost function from income function as:
Therefore, thefunction for profit would be
d.
To find:
What is the profit when you make and sell 100 birdhouses?
d.
Answer to Problem 29E
You will make a profit of $1000.
Explanation of Solution
Given:
You make and sell birdhouses. Your fixed cost for your tools and workspace are $3000. The cost of wood and other materials needed to make a birdhouse is $10. You sell each birdhouse for $50.
Calculation:
To find the profitwhen you make and sell 100 birdhouses, we will substitute
Therefore, you will make a profit of $1000.
e.
To find:
How many birdhouses do you need to make and sell in order to break even?
e.
Answer to Problem 29E
You need to make and sell 75 birdhouses in order to break even.
Explanation of Solution
Given:
You make and sell birdhouses. Your fixed cost for your tools and workspace are $3000. The cost of wood and other materials needed to make a birdhouse is $10. You sell each birdhouse for $50.
Calculation:
We know that breakeven is a point, where you make a profit of $0.
To find the break even, we will equate profit function with 0 and solve for xas :
Therefore, you need to make and sell 75 birdhouses in order to break even.
Chapter 8 Solutions
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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