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Extra info for Calculus for Business Economics & the Social & Life Sciences, Brief 10th Edition
43. CONSUMER EXPENDITURE Suppose x ϭ Ϫ200p ϩ 12,000 units of a particular commodity are sold each month when the market price is p dollars per unit. The total monthly consumer expenditure E is the total amount of money spent by consumers during each month. a. Express total monthly consumer expenditure E as a function of the unit price p and sketch the graph of E( p). b. Discuss the economic significance of the p intercepts of the expenditure function E( p). c. Use the graph in part (a) to determine the market price that generates the greatest total monthly consumer expenditure.
3 LINEAR FUNCTIONS Solution 4 By rewriting the equation 4x ϩ 3y ϭ 3 in the slope-intercept form y ϭ Ϫ x ϩ 1, we 3 4 see that L has slope m L ϭ Ϫ . 3 4 a. Any line parallel to L must also have slope m ϭ Ϫ . The required line L1 3 contains P(Ϫ1, 4), so 4 y Ϫ 4 ϭ Ϫ (x ϩ 1) 3 4 8 yϭϪ xϩ 3 3 b. A line perpendicular to L must have slope m ϭ Ϫ 1 3 ϭ . 29. 29 Lines parallel and perpendicular to a given line L. 3 In Exercises 1 through 8, find the slope (if possible) of the line that passes through the given pair of points.
Express the manufacturer’s monthly profit as a function of price, graph this function, and use the graph to estimate the optimal selling price. 40. MANUFACTURING COST A manufacturer can produce tires at a cost of $20 apiece. It is estimated that if the tires are sold for p dollars apiece, consumers will buy 1,560 – 12p of them each month. Express the manufacturer’s monthly profit as a function of price, graph this function, and use the graph to determine the optimal selling price. How many tires will be sold each month at the optimal price?
Calculus for Business Economics & the Social & Life Sciences, Brief 10th Edition by Gerald_Bradley