Section 68 problems 3 5 12 2 section 69 problem 10 3

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1. Section 6.8 Problems 3, 5, 122. Section 6.9 Problem 103. Section 6.10 Problem 54. Section 6.11 Problems 4, 5, 85. Section 7.1 Problem 66. Section 7.3 Problem 17. Section 7.4 Problems 6, 98. Section 7.7 Problems 1, 59. Section 8.2 Problems 5, 6, 710. Section 8.4 Problem 211. Section 8.5 Problems 3, 512. Section 8.6 Problems 2, 613. Section 8.7 Problems 3, 5The remaining problems mostly relate chapter 8 to some earlier economics concepts.14. Find the quantity which maximizes profit if the total revenue and total cost (in dollars) are given byR(q) = 5q-0.003q2C(q) = 300 + 1.1qwhereqis the quantity and 0q1000 units. What production level gives the minimum profit?15. The total revenue and total cost curves for a product are given in Figure below.(a) Sketch the marginal revenue and marginal cost, MR and MC, on the same axes. Mark the two quantitieswhere marginal revenue equals marginal cost. What is the significance of these two quantities? At whichquantity is profit maximized?(b) Sketch the profit functionπ(q).q3q4q(quantity)$R(q)C(q)
16. Show that if marginal cost is greater than average cost, then the derivative of average cost with respect to quantityis positive.17. Ifa(t) andb(t) are positive valued differentiable functions, and ifA, α, βare constants find expressions fory0y.(a)y= (a(t))2b(t)(b)y=a(t)5b(t)(c)y=A(a(t))α(b(t))β, whereAis a constant.18. IfF(x) =f(xng(x)), find a formula forF0(x).19. For the total cost functionC(y) =y2-3y+ 2, y >0show that and (illustrate on a graph)(a) Marginal cost (MC) is less than average cost (AC) when average cost is decreasing(b)MC=ACwhen the derivative ofACis zero.(c)MCexceedsACwhenACis increasing.20. A store has been selling 200 DVD burners a week at $350 each.A market survey indicates that for each $10rebate offered to buyers, the number of units sold will increase by 20 a week. Find the demand function and therevenue function. How large a rebate should the store offer to maximize its revenue?21.(a) Show that the critical points of an average cost function occur when the marginal cost equals the averagecost.(b) IfC(x) = 16000 + 200x+ 4x3/2, in dollars, find (i) the cost, average cost, and marginal cost at a productionlevel of 1000 units (ii) the production level that minimizes the average cost (iii) the minimum average cost.22.(a) Show that if the profit is at a maximum, then the marginal revenue equals the marginal cost.(b) IfC(x) = 16000 + 500x-1.6x2+ 0.004x3is the cost function andp(x) = 1700-7xis the demand function,find the production level that maximizes the profit.

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Term
Spring
Professor
Johns
Tags
Math, Derivative, Supply And Demand, lim, used car

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