Explanation Given Information: The weekly costs function of a small business are represented by, C = 100 + 30 x + x 2 10 , where x represents the number of units produced by the firm per month. The selling price of the product is $ 46 per unit. Formula used: The simple power rule for the derivative, d d x ( x n ) = n x n − 1 The rule of derivative for constant multiplication, d d x [ k f ( x ) ] = k d d x [ f ( x ) ] The sum or difference rule of the derivative, d d x [ f ( x ) + g ( x ) ] = d d x [ f ( x ) ] + d d x [ g ( x ) ] Calculation: Consider the provided cost function for the small business is, C = 100 + 30 x + x 2 10 . The revenue earned from one unit of the product is $46. Thus, for x units of the product, the revenue function is represented as, R ( x ) = 46 x The profit function is the difference of the revenue function and cost functions, P ( x ) = R ( x ) − C ( x ) Substitute 40 x for R ( x ) and 100 + 30 x + x 2 10 for C ( x ) . P ( x ) = R ( x ) − C ( x ) = 46 x − 100 − 30 x − x 2 10 = 16 x − 100 − x 2 10 Therefore, the profit function is P ( x ) = 16 x − 100 − x 2 10

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Chapter 9, Problem 107RE

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To calculate: The marginal profit for the small business that has a weekly cost function, C=100+30x+x210 where x is the number of units produced each week and the competitive market price of the product is $46.

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Chapter 9, Problem 106RE

Chapter 9, Problem 108RE

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Chapter 9 Solutions

MATHEMATICAL APPL F/MGMT LIFE (LL) FDS

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The marginal profit for the small business that has a weekly cost function, C = 100 + 30 x + x 2 10 where x is the number of units produced each week and the competitive market price of the product is $ 46 .

Solution Summary: The author calculates the marginal profit for the small business that has a weekly cost function, C=100+30x+x210.

To calculate: The marginal profit for the small business that has a weekly cost function, C=100+30x+x210 where x is the number of units produced each week and the competitive market price of the product is $46.

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Chapter 9 Solutions