- 142 Hmwk
copyright Spring 2008 Amy Collins
1
Homework # 5, Part I
1. pg. 180 #28 2. pg. 180 #10 3. pg. 181 #31-38 4. Let R(x) be the revenue (in dollars) from the sale of x car seats, and suppose that the slope of the secant line through (x, R(x)) and (x + h, R(x + h)) is given by R(x + h) - R(x) = 60 - 0.05x - 0.0025h. h (a) Find the average change in revenue if production is increased from 1,000 car seats to 1,050 car seats. (Hint: What should x and h be in the above equation?) (b) Find the instantaneous rate of change of revenue at a production level of 1,000 car seats.
Homework # 5, Part II
1. Find the indicated derivatives. (Simplify answers by using positive exponents only.) d 3 2 4 3 3x + - x dx x t - t dS (b) if S(t) = dt t (a) 2. If h(x) = 4f (x) - 2g(x) + 3, f (5) = 4, and g (5) = -8, what is h (5)? 3. pg. 189 #24 4. pg. 189 #52 5. The profit (in dollars) from the sale of x car seats for infants is given by P (x) = 45x - 0.025x2 - 5000 , 0 x 2400. (a) Find the average change in profit if production is increased from 800 car seats to 850 car seats. (b) Find marginal profit. (c) Find the (instantaneous) rate of change of profit at a production level of 800 car seats. (d) What is the approximate profit from producing the 801st car seat? 6. The total of sales a company (in millions of dollars) t months from now are given by S(t) = 0.015t4 + 0.4t3 + 3.4t2 + 10t - 3. (a) Find total sales after 4 months. (b) After 4 months, by how much are total sales increasing?
142 - Hmwk
copyright Spring 2008 Amy Collins
2
7. A particular book is sold at a price determined by the demand function p(x) = -0.5x + 50. It costs $7 to produce each book, and there are $275 of fixed costs associated with producing the books. If x represents the number of books made and sold, find the following: (a) The exact cost, revenue, and profit produced by the 20th book (b) The estimated cost, revenue, and profit produced by the 20th book (use marginal analysis) 8. On our course webpage under "Homework problems", click on the &quo...