Explanation Given: Colin sold 100 pies when the its price was $5 and he sold 40 pies when the price was $10. Calculation: Consider the linear function as follows, N ( P ) = a P + b ………(1) where a and b are constants. According to the given conditions, N ( 5 ) = 100 and N ( 10 ) = 40 Substitute 5 for P and 100 for N ( P ) in equation(1). N ( 5 ) = 100 5 a + b = 100 ………..(2) Substitute 510 for P and 40 for N ( P ) in equation(1). N ( 10 ) = 40 10 a + b = 40 ………..(3) Subtract equation (2) from equation (3) to find the value of a. 10 a + b = 40 − 5 a + b = 100 5 a = − 60 ¯ The value of a is − 12

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.2, Problem 28E

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The linear demand function N for Colin’s kidney pies as a function of P. And find the revenue for P=5,6,7,8,9,10 and a price that maximize the revenue.

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Chapter 1.2, Problem 27E

Chapter 1.2, Problem 29E

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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The linear demand function N for Colin’s kidney pies as a function of P. And find the revenue for P = 5 , 6 , 7 , 8 , 9 , 10 and a price that maximize the revenue.

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The linear demand function N for Colin’s kidney pies as a function of P. And find the revenue for P=5,6,7,8,9,10 and a price that maximize the revenue.

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Chapter 1 Solutions