<p> Math 141 Week in Review Sections 1.1-1.4 9/5/05</p><p>Section 1.2.</p><p>1. Find the slope of the line shown in the figure.</p><p>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?</p><p>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).</p><p>4. Write the equation in slope-intercept form, and find the slope and y-intercept of the corresponding line: y + 6 = 0.</p><p>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.</p><p>7. Find an equation of the line passing through the point (c, d) with slope 0.</p><p>8. Sketch the straight line by finding the x- and y-intercepts: 3x – 5y = 20</p><p>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.</p><p> a. What is the slope of the line? What does it represent?</p><p> b. What is the S-intercept of the line? What does it represent?</p><p>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).</p><p>Year x 0 1 2 3 4 Annual Sales, y 2.8 4.1 5.3 6.2 7.6</p><p> 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.</p><p> d. Use the equation found in part (c) to estimate the annual sales of equipment in 2002.</p><p>Section 1.3</p><p>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</p><p>2. Determine whether the equation defines y as a linear function of x. x - 5y = 2</p><p>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.</p><p> a. What is the cost function?</p><p> b. What is the revenue function?</p><p> c. What is the profit function?</p><p> d. Compute the profit (loss) corresponding to production levels of 2000, 6000, and 10,000 cameras, respectively.</p><p>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.</p><p>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.</p><p>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?</p><p>Section 1.4</p><p>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. </p><p>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.</p><p>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?</p><p>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</p><p>6. Find the equilibrium quantity and price for the computer chip company described in Section 1.3, #6 and #8 above.</p>