Math 141 Week in Review

Math 141 Week in Review Sections 1.1-1.4 9/5/05

Section 1.2.

1. Find the slope of the line shown in the figure.

2. Given the equation 3x - 2y = 7, answer the following questions: a. If x increases by 1 unit, what is the corresponding change in y? b. If x decreases by 2 units, what is the corresponding change in y?

3. Find an equation of the vertical line that passes through (0, 8). Find an equation of the vertical line that passes through (2, 7).

4. Write the equation in slope-intercept form, and find the slope and y-intercept of the corresponding line: y + 6 = 0.

5. Write the equation in slope-intercept form, and find the slope and y-intercept of the corresponding line: 8x + 5y – 24 = 0. 6. Find an equation of the line passing through the point (c, d) with undefined slope.

7. Find an equation of the line passing through the point (c, d) with slope 0.

8. Sketch the straight line by finding the x- and y-intercepts: 3x – 5y = 20

9. A mathematical model for a pharmaceutical company’s sales, in billions of dollars, is given by S = 5.74 + 0.97x where x = 0 corresponds to 1988.

a. What is the slope of the line? What does it represent?

b. What is the S-intercept of the line? What does it represent?

10. The sales (in millions of dollars) of a company’s equipment sales from 2000 through 2004 is given below (x = 0 corresponds to 2000).

Year x 0 1 2 3 4 Annual Sales, y 2.8 4.1 5.3 6.2 7.6

a. Plot the annual sales (y) versus the year (x). b. Draw a straight line L through the points corresponding to 2000 and 2004. c. Derive an equation of the line L.

d. Use the equation found in part (c) to estimate the annual sales of equipment in 2002.

Section 1.3

1. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 3x = 2y - 7

2. Determine whether the equation defines y as a linear function of x. x - 5y = 2

3. An automobile purchased for use by the manager of a firm at a price of $26,000 is to be depreciated using the straight-line method over 5 yr. What will be the book value of the automobile at the end of 2 yr? 4. A camera manufacturer has a monthly fixed cost of $26,000 and a production cost of $12 for each camera manufactured. The cameras sell for $18 each.

a. What is the cost function?

b. What is the revenue function?

c. What is the profit function?

d. Compute the profit (loss) corresponding to production levels of 2000, 6000, and 10,000 cameras, respectively.

5. Sketch the equation of the demand curve 4p + 5x – 60 = 0, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars. Determine the quantity demanded corresponding to the unit price $12.

6. The quantity demanded for a certain computer chip is 3000 units when the unit price is set at $20. The quantity demanded is 5200 units when the unit price is $13. Find the demand equation if it is known to be linear. 7. Sketch the equation of the supply curve ½x – ¾p + 8 = 0, where x represents the quantity supplied in units of 1000 and p is the unit price in dollars. Determine the number of units of the commodity the supplier will make available in the market at the unit price $20.

8. The manufacturer will make 2500 of the computer chips in problem #6 available when the price is $18. At a unit price of $15, 1800 chips will be marketed. Find the supply equation if the equation is known to be linear. How many chips will be marketed when the unit price is $22?

Section 1.4

1. Find the point of intersection of the pair of straight lines: 2x + 3y = 12 5x – 2y = 11 2. Find the break-even point for the firm whose cost function C and revenue function R were found in Section 1.3, #4 above.

3. A company manufactures microwave ovens. Each oven sells for $60. The monthly fixed costs total $24,000, and the variable cost of producing each oven is $8. Find the break-even point for the company.

4. The sales for Maddie’s Beauty Supply are expected to be given by S = 3.2 + .04t thousand dollars t years from now. The annual sales of Jean’s Beauty Supply are expected to be given by S = 1.4 + .05t thousand dollars t years from now. When will Jean’s annual sales first surpass Maddie’s annual sales?

5. Find the equilibrium quantity and price for the supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars: 4x + 5p – 50 = 0 and 6x – 3p + 15 = 0

6. Find the equilibrium quantity and price for the computer chip company described in Section 1.3, #6 and #8 above.