Pro forma income statement The marketing department of Metroline Manufacturing estimates that its sales in 2016 will be $\$ 1.5$ million. Interest expense is expected to remain unchanged at $\$ 35,000$, and the firm plans to pay $\$ 70,000$ in cash dividends during 2016. Metroline Manufacturing's income statement for the year ended December 31,2015 , and a breakdown of the firm's cost of goods sold and operating expenses into their fixed and variable components are given below.

a. Use the percent-of-sales method to prepare a pro forma income statement for the year ended December $31,2016$.

Metroline Manufacturing
Income Statement
for the Year Ended December 31, 2015
Sales revenue	$1,400,000
Less: Cost of goods sold	910,000
Gross profits	$ 490,000
Less: Operating expenses	120,000
Operating profits	$370,000
Less: Interest expense	35,000
Net profits before taxes	$ 335,000
Less: Taxes (rate = 40%)	134,000
Net profits after taxes	$201,000
Less: Cash dividends	66,000
To retained earnings	$ 135,000

Metroline Manufacturing
Breakdown of Costs and Expenses
into Fixed and Variable Components
for the Year Ended December 31, 2015
Cost of goods sold
Fixed cost	$210,000
Variable cost	700,000
Total costs	$910,000
Operating expenses
Fixed expenses	$36,000
Variable expenses	84,000
Total expenses	$120,000

Find $I_z$ for the given lamina with uniform density of $1$ . Use a computer algebra system to verify your results.

$$z=x^2+y^2, \quad 0 \leq z \leq h$$

A popular shoe store sold 5,700 pairs of athletic shoes in 2008. Projections are for a 3% increase in sales each year for several years after 2008. What is the projected total sales (number of athletic shoes sold). during the period from 2008 to 2015?

Consider the function f(x,y)=xy, for x $\geq$ 0 and y $\geq$ 0.

Make a conjecture about the relationship between the graphs of f and g(x, y)=-f(x, y). Use a computer algebra system to confirm your answer.

A day’s sales in $\$1000$ units at a gas station have a gamma distribution with parameters $k = 5$ and $\lambda = 0.9$. If the sales on different days are distributed independently of each other, estimate the probability that in one year the gas station takes in more than $\$2$ million.

Use a computer algebra system, if available, to evaluate the expressions that follow. (We will see in the next section how a calculator can be used to evaluate such expressions.)

$$\log _{0.9} 2$$

When priced at $30 each, a toy has annual sales of 4,000 units. The manufacturer estimates that each$1 increase in price will decrease sales by 100 units. Find the unit price that will maximize total revenue. (Total revenue = price * number of units sold.)

In given problem, find the indicated limit. In most cases, it will be wise to do some algebra first.

$$\lim _{x \rightarrow-1} \frac{x^3-4 x^2+x+6}{x+1}$$

The Luncheonette rents a 30-foot by 50-foot area at the Nottingham Mall. The Luncheonette pays $9.20 per square foot per year plus 2% of gross sales. Last year The Luncheonette had$225,000 in gross sales. What was its monthly rent?

In the following exercise, sketch several representative vectors in the vector field. Use a computer algebra system to verify your results.

$$\mathbf{F}(x, y)=\mathbf{i}-2 y \mathbf{j}$$

The sale price of the new car was $18,500. The sales-tax rate was 6.5 percent. a. What was the sales tax on the car? b. What was the total price including tax? c. If the commission paid to a salesperson is 2 percent of the sale price, how much is the commission on a$18,500 sale?

Use a computer algebra system, if available, to evaluate the expressions that follow. (We will see in the next section how a calculator can be used to evaluate such expressions.)

$$\log _5 30$$

Simplify the expression

$$Y=A \cdot \bar{B} \cdot \bar{C}+A \cdot \bar{B} \cdot C+\bar{A} \cdot B \cdot C+A \cdot B \cdot C$$

using the boolean algebra.