A hand tool manufacturer produces a product for which the variable cost is $\$ 5.35$ per unit and the fixed costs are $\$ 16,000$. The company sells the product for $\$ 8.20$ and can sell all that it produces. Find the total cost as a function of $x$, the number of units produced.

Kylie’s Cookies is considering the purchase of a larger oven that will cost $2,200 and will increase her fixed costs by$59. What would happen if she purchased the new oven to realize the variable cost savings of $0.10 per cookie, and what would happen if she raised her price by just$0.20? She feels confident that such a small price increase will decrease the sales by only 25 units and may help her offset the increase in fixed costs. Given the following current prices how would the break-even in units and dollars change if she doesn’t increase the selling price and if she does increase the selling price? Complete the monthly contribution margin income statement for each of these cases.

$$\begin{array}{lr} \hline &\textbf{With Current}&\textbf{With Decreased VC}&\textbf{With Increased SP,}\\ &\textbf{Price}&\textbf{and Increased FC}&\textbf{Decreased VC and}\\ &&&\textbf{Increased FC}\\ \hline \text { Sales price per unit } & \$1.75 \\ \text { Variable cost per unit } & 0.40 \\ \text { Contribution margin per unit } & \$ 1.30 \\ \text { Fixed costs } & \$ 405\\ \text{}\\ \text { Break-even in units } &300 \\ \text { Break-even in dollars } & \$525 \end{array}$$

$$\begin{array}{c} \hline\textbf{Monthly Contribution Margin Income Statement}\\ \hline \end{array}$$

$$\begin{array}{lc} \text{Unit sales, expected}&800\\ \text{Sales}\\ \text{Variable costs}\\ \text{Contribution margin}\\ \text{Fixed costs}\\ \text{Net income}\\ \end{array}$$

Donner Corporation estimates that to produce wooden baseball bats, it must spend $\$ 38,160$ in fixed costs. The company estimates that the variable costs will be $\$ 14.89$ for each bat. The selling price of the bats is to be $\$ 50.89$ each. a. At that selling price, how many of the bats must be sold to break even? b. To break even, the company must have a sales income of what amount from this operation?

Under absorption costing, a company had the following per unit costs when 10,000 units were produced.

$$\begin{array}{lr} \text{Directlabor}&\text{\$ 2}\\ \text{Direct materials}&\text{3}\\ \text{Variable overhead}&\underline{\text{\hspace{5pt}4}}\\ \text{Total variable cost}&\text{9}\\ \text{Fixed overhead (\$50,000/10,000 units)}&\underline{\text{\hspace{5pt}5}}\\ \text{Total product cost per unit}&\underline{\underline{\text{\$14}}}\\ \end{array}$$

The company sells its product for $50 per unit. Due to new regulations, the company must now incur$2 per unit of hazardous waste disposal costs and $8,500 per year of fixed hazardous waste disposal costs. Compute the contribution margin per unit. including hazardous waste disposal costs.

The following exercise demonstrate applications of linear functions. Analyze the information given to determine the equation of the relevant line or lines. Use the linear equation to determine the requested information. The Tie Shop sells its ties for $21 each. The shop has weekly fixed costs of$845, and each tie costs $12. How many ties must be sold to make a profit?

A manufacturer is planning to sell a new product at the price of $150 per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, approximately

$$\frac{320 y}{y+2}+\frac{160 x}{x+4}$$

units of the product will be sold. The cost of manufacturing the product is $50 per unit. If the manufacturer has a total of$8,000 to spend on development and promotion, how should this money be allocated to generate the largest possible profit?

[Hint: Profit = (number of units)(price per unit - cost per unit) - the amount spent on development and production.]

Rainbow Tours provides walking tours of Springfield. Rainbow charges $40 per person for the tour and incurs$16 in variable costs for labor, drinks, and maps. The monthly fixed costs for Rainbow Tours are $3,600.

Required
Rainbow Tours’s owner believes that 175 people a month will sign up for the walking tour. What is the margin of safety in terms of the number of people signing up for the tour?

If Intervale Railway’s fixed costs total $90,000 per month, the variable cost per passenger is$45, and tickets sell for $75, what is the breakeven point in units? a. 1,200 passengers b. 2,000 passengers c. 225,000 passengers d. 3,000 passengers

The annual fixed costs for owning a small sedan are $1289, assuming the car is completely paid for. The cost to drive the car is approximately$0.15 per mile. Write a linear equation that relates the cost C and the number x of miles driven annually.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. Discuss the pros and cons of each loan.

You need a $\$ 180,000$ loan.

$\quad$ Option $1$: a $30$-year loan at an $\mathrm{APR}$ of $7.25 \%$

$\quad$ Option $2$: a $15$-year loan at $6.8\%$

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. Discuss the pros and cons of each loan.

You need a $\$ 75,000$ loan.

$\quad$ Option $1$: a $30$-year loan at an $\mathrm{APR}$ of $8 \%$

$\quad$ Option $2$: a $15$-year loan at $7 \%$

Under absorption costing, a company had the following per unit costs when 10,000 units were produced.

$$\begin{array}{lr} \text{Directlabor}&\text{\$ 2}\\ \text{Direct materials}&\text{3}\\ \text{Variable overhead}&\underline{\text{\hspace{5pt}4}}\\ \text{Total variable cost}&\text{9}\\ \text{Fixed overhead (\$50,000/10,000 units)}&\underline{\text{\hspace{5pt}5}}\\ \text{Total product cost per unit}&\underline{\underline{\text{\$14}}}\\ \end{array}$$

The company sells its product for $50 per unit. Due to new regulations, the company must now incur$2 per unit of hazardous waste disposal costs and $8,500 per year of fixed hazardous waste disposal costs. Compute the company's break-even point (in units). including hazardous waste disposal costs.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. Discuss the pros and cons of each loan.

You need a $\$ 60,000$ loan.

$\quad$ Option $1$: a $30$-year loan at an $\mathrm{APR}$ of $7.15 \%$

$\quad$ Option $2$: a $15$-year loan at $6.75\%$

Write the revenue function, R. A company that manufactures small canoes has a fixed cost of $18,000. It costs$20 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.)