AP37. The production function f(x) gives the number of units of an item that a manufacturing company canproduce from x units of raw material. The company buys the raw material at price w dollars per unit andsells all it produces at a price of p dollars per unit. The quatity of raw material that maximizes profit isdenoted by x.(d) Assuming it is nozero, is f"(x) positive or negative?(e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat xas a function of w. Find a formula for the derivative dx"/dw and decide whether it is positive ornegative.(f) If the price w goes up, should the manufacturing company buy more or less of the raw material?

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AP37. The production function f(x) gives the number of units of an item that a manufacturing company can produce from x units of raw material. The company buys the raw material at price w dollars per unit and sells all it produces at a price of p dollars per unit. The quantity of raw material that maximizes profit is denoted by x. (d) Assuming it is nonzero, is f"(x) positive or negative? (e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat x as a function of w. Find a formula for the derivative dx'/dw and decide whether it is positive or negative. (f) If the price w goes up, should the manufacturing company buy more or less of the raw material?

AP37. The production function f(x) gives the number of units of an item that a manufacturing company can produce from x units of raw material. The company buys the raw material at price w dollars per unit and sells all it produces at a price of p dollars per unit. The quantity of raw material that maximizes profit is denoted by x. (d) Assuming it is nonzero, is f"(x) positive or negative? (e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat x as a function of w. Find a formula for the derivative dx'/dw and decide whether it is positive or negative. (f) If the price w goes up, should the manufacturing company buy more or less of the raw material?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.CR: Chapter Review

Problem 16E: Digital cameras A company that produces and sells digital cameras has determined that the total...

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