Conn Man’s Shops, a national clothing chain, had sales of $350 million last year. The business has a steady net profit margin of 9 percent and a dividend payout ratio of 25 percent. The balance sheet for the end of last year is shown next. The firm’s marketing staff has told the president that in the coming year there will be a large increase in the demand for overcoats and wool slacks. A sales increase of 20 percent is forecast for the company. All balance sheet items are expected to maintain the same percent-of-sales relationships as last year,* except for common stock and retained earnings. No change is scheduled in the number of common stock shares outstanding, and retained earnings will change as dictated by the profits and dividend policy of the firm. (Remember the net profit margin is 9 percent.). What would be the need for external financing if the net profit margin went up to 10.5 percent and the dividend payout ratio was increased to 60 percent? Explain.

Balance Sheet, End Of Year ( in$ millions)
Assets		Liabilities and Stockholders’ Equity
Cash	$\$25$	Accounts payable	$\$ 64$
Accounts receivable	$40$	Accrued expenses	$31$
Inventory	$28$	Other Payables	$45$
Plant and equipment	$133$	Common stock	$50$
Total assets	$\$280$
		Retained earnings	$90$
		Total liabilities and stockholders’ equity	$\$280$

A salesman's monthly gross pay consists of $3500 plus 20 percent of the dollar amount of his sales. If his gross pay for one month was$15,500, what was the dollar amount of his sales for that month? $$ F \ $12,000 $$ $$ G \ $16,000 $$ $$ H \ $60,000 $$ $$ J \ $70,000 $$

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.)

$$\log _{19} 5$$

By using a computer algebra system to solve the cubic equation

$$x^3+x+1=3+ε,$$

find the largest possible value of δ that works for any given ε > 0.

In the following exercise, use a computer algebra system to find the curl F for the vector field.

$$\mathbf{F}(x, y, z)=\sqrt{x^2+y^2+z^2}(\mathbf{i}+\mathbf{j}+\mathbf{k})$$

In this exercise, use a computer algebra system to analyze and graph the function. Identify any relative extrema, points of inflection, and asymptotes.

$$f(x)=\frac{20 x}{x^2+1}-\frac{1}{x}$$

The Alliance Corp. expects to sell the following number of units of copper cables at the prices indicated, under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?

Outcome	Probability	Units	Price
A	$0.70$	225	$\$ 20$
B	$0.10$	370	35
C	$0.20$	510	45

Using De Morgan's theorems and the rules of boolean algebra, simplify the following logic function:

$$F(X, Y, Z)=\bar{X} \cdot \bar{Y} \cdot \bar{Z}+\bar{X} \cdot Y \cdot Z+X \cdot(\overline{Y+Z})$$

Use a computer algebra system to find the indicated Taylor polynomials for the function f. Graph the function and the Taylor polynomials. \

$$f(x)=\frac{1}{x^2+1}$$

$n=4, \quad c=0$

Identify and sketch the quadric surface. Use a computer algebra system to confirm your sketch.
$16 x^2+9 y^2+16 z^2-32 x-36 y+36=0$

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.

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

Use Maple or another computer algebra system to evaluate and simplify the derivatives of the functions. $\left.\frac{d}{d x} \frac{x \cos (x \sin x)}{x+\cos (x \cos x)}\right|_{x=0}$

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.)

$$\log _5 30$$