2.6 What is the point of intersection of the graphs called?
2.7 Explain what is meant by this point of intersection.
2.8 How many bags must Shelly sell to start showing a profit?
2.9 Calculate the amount of profit on 17 bags. Show all your calculations.

Income and expenses for Shelley’s Bags

Question

2.6 What is the point of intersection of the graphs called?
2.7 Explain what is meant by this point of intersection.
2.8 How many bags must Shelly sell to start showing a profit?
2.9 Calculate the amount of profit on 17 bags. Show all your calculations.

Income and expenses for Shelley’s Bags

UpStudy AI · Accepted Answer

$$ \textbf{2.6} $$ The graphs intersect at the break‐even point.

$$ \textbf{2.7} $$ This point of intersection is where the total income equals the total expenses. In other words, at the break‐even point the money earned from selling bags exactly covers all the costs, so there is neither a profit nor a loss.

For the next parts we use the typical income–expense model for Shelley's Bags. Suppose that the income from selling one bag is $$\$11$$ per bag, and the expenses consist of a fixed cost of $$\$60$$ plus a variable cost of $$\$6$$ per bag. (That is, if $$x$$ represents the number of bags sold, then)

$$
\text{Income: } I(x)=11x
$$
$$
\text{Expenses: } E(x)=60+6x
$$

$$ \textbf{2.8} $$ To find the break‐even point, set the income equal to the expenses:

$$
11x = 60+6x
$$

Subtract $$6x$$ from both sides:

$$
11x-6x = 60
$$
$$
5x=60
$$

Divide both sides by 5:

$$
x=\frac{60}{5}=12
$$

So, the break‐even point is at 12 bags. However, to start showing a profit, Shelly must sell more than 12 bags. Therefore, she must sell at least $$12+1=13$$ bags.

$$ \textbf{2.9} $$ To calculate the profit when 17 bags are sold, first compute the income and the expenses for 17 bags.

$$
\text{Income for 17 bags: } I(17)=11\times17=187
$$
$$
\text{Expenses for 17 bags: } E(17)=60+6\times17=60+102=162
$$

The profit $$P$$ is given by the difference between income and expenses:

$$
P=I(17)-E(17)=187-162=25
$$

Thus, if Shelly sells 17 bags, her profit is $$\$25$$.
2.6 The point where the income and expenses graphs meet is called the break-even point. 2.7 At the break-even point, Shelly's income exactly equals her expenses, resulting in neither profit nor loss. 2.8 Shelly must sell at least 13 bags to start showing a profit. 2.9 Selling 17 bags results in a profit of \$25.

2.6 What is the point of intersection of the graphs called?
2.7 Explain what is meant by this point of intersection.
2.8 How many bags must Shelly sell to start showing a profit?
2.9 Calculate the amount of profit on 17 bags. Show all your calculations.

Income and expenses for Shelley’s Bags

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2.6 What is the point of intersection of the graphs called? 2.7 Explain what is meant by this point of intersection. 2.8 How many bags must Shelly sell to start showing a profit? 2.9 Calculate the amount of profit on 17 bags. Show all your calculations. Income and expenses for Shelley’s Bags

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Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

2.6 What is the point of intersection of the graphs called?
2.7 Explain what is meant by this point of intersection.
2.8 How many bags must Shelly sell to start showing a profit?
2.9 Calculate the amount of profit on 17 bags. Show all your calculations.

Income and expenses for Shelley’s Bags