60Suppose the demand function for x thousand of a certain item is p= 140 + , where x>1 and p is in dollars.In x'(a) Find the marginal revenue.(b) Find the revenue from the next thousand items at a demand of 5000 (x = 5).(a) The marginal revenue function is R'(x)=(Use integers or fractions for any numbers in the expression.)

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Answered: 60 Suppose the demand function for x…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The marginal average cost of producing x digital sports watches is given by the function -1800 AC' (æ) = , AC(100) = 23. The fixed cost is A. $2000. B. $1800. C. $2500. D. $1900. Select one: O A O B O C O D
0.9 The profit in dollars from the sale of x expensive watches is P(x)- 0.04x-2x+7x -5000. Find the marginal profit when (a) x=D100, (b) x- 2000, (c) x-5000 and (d) x- 10,000. (a) When x= 100, the marginal profit is $ (Round to the nearest integer as needed)
An economist is interested in how the price of a certain item affects its sales. When the price of the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand") Suppose we found out that f(150) = 2,000 and that f'(150) = -25. (a) Sketch the information of two boldface statements in a quick picture/sketch: (b) Write out in words what the first statement f(150) = 2,000 means in the context. (c) The fact that the derivative is negative reflects what natural phenomenon? (d) Write out in words what the statement f'(150) = -25 means in the context. (Add in appropriate units!) (e) Use the information given to estimate f(151) and f(149.5). Show your work, and explain your rationale for proceeding as you did. A little picture would be ideal to explain your thinking.
Assume that it costs a company approximately C(x) = 400,000 + 120x + 0.002x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.

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