Explanation Given: The expression for functions S ( q ) and D ( q ) , S ( q ) = q 2 + 5 q + 100 D ( q ) = 350 − q 2 Formula used: Write the formula for integral of a power function. The integral for the function f ( x ) = x n provided n ≠ − 1 is given by the formula: ∫ x n d x = x n + 1 n + 1 + C The integral for the function f ( x ) = k , k being a real number is given by the formula: ∫ k d x = k x + C . In the above formulae, C is the integration constant. The use of integration constant C is done only for indefinite integrals. The definite integral of a function f ′ ( x ) from x = a to x = b is calculated by the formula: ∫ a b f ′ ( x ) d x = | f ( x ) | a b = f ( b ) − f ( a ) Calculation: Consider the given functions: S ( q ) = q 2 + 5 q + 100 D ( q ) = 350 − q 2 Calculate the equilibrium point where S ( q ) = D ( q ) . q 2 + 5 q + 100 = 350 − q 2 2 q 2 + 5 q − 250 = 0 2 q 2 + 25 q − 20 q − 250 = 0 q ( 2 q + 25 ) − 10 ( 2 q + 25 ) = 0 Solve for q . ( q − 10 ) ( 2 q + 25 ) = 0 q − 10 = 0 or 2 q + 25 = 0 q = 10 or q = − 25 2 . Discard the negative value of q . Write the equation for supply function. S ( q ) = q 2 + 5 q + 100

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 13, Problem 73RE

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To calculate: The producers’ surplus, if the supply function S(q) and demand function D(q) are given by the equations below:

S(q)=q2+5q+100D(q)=350−q2

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Chapter 13, Problem 72RE

Chapter 13, Problem 74RE

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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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The producers’ surplus, if the supply function S ( q ) and demand function D ( q ) are given by the equations below: S ( q ) = q 2 + 5 q + 100 D ( q ) = 350 − q 2

Solution Summary: The author explains the formula used to calculate the producers' surplus, which is 916.67.

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To calculate: The producers’ surplus, if the supply function S(q) and demand function D(q) are given by the equations below:

S(q)=q2+5q+100D(q)=350−q2

Want to see the full answer?

Chapter 13 Solutions

The producers’ surplus, if the supply function S ( q ) and demand function D ( q ) are given by the equations below: S ( q ) = q 2 + 5 q + 100 D ( q ) = 350 − q 2

Solution Summary: The author explains the formula used to calculate the producers' surplus, which is 916.67.

Concept explainers

Videos

To calculate: The producers’ surplus, if the supply function S(q) and demand function D(q) are given by the equations below: S(q)=q2+5q+100D(q)=350−q2

Want to see the full answer?

Chapter 13 Solutions

To calculate: The producers’ surplus, if the supply function S(q) and demand function D(q) are given by the equations below:

S(q)=q2+5q+100D(q)=350−q2