   Chapter 12.4, Problem 9E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-12, cost, revenue, and profit are in dollars and x is the number of units.Suppose that the marginal revenue for a product is M C ¯ = 900 and the marginal cost is M C ¯ = 30 x + 4 , with a fixed cost of $1000.(a) Find the profit or loss from the production and sale of 5 units.(b) How many units will result in a maximum profit? (a) To determine To calculate: The profit or loss from the production and sale of 5 units if the marginal revenue for a product is MR¯=900 and marginal cost of the product is MC¯=30x+4 and fixed cost is$1,000.

Explanation

Given information:

The marginal revenue for a product is MR¯=900 and

Marginal cost of the product is MC¯=30x+4 and

Fixed cost is $1,000. Formula used: Total Cost: C(x)=MC¯dx Where MC¯ is defined as the marginal cost. Total Revenue: R(x)=MR¯dx Where MR¯ is defined as the marginal revenue. Profit: The profit function P(x) is defined as the revenue function R(x) minus the cost function C(x) P(x)=R(x)C(x) Integral formula, xndx=xn+1n+1+K Calculation: Consider the provided data, The marginal cost: MC¯=30x+4 And marginal revenue MR¯=900 Consider the formula of revenue function: R(x)=MR¯dx Substitute 900 for MR¯ in above equation and evaluate by the use of the integral formula xndx=xn+1n+1+K As, R(x)=900dx=900x Now, consider the formula of cost function: C(x)=MC¯dx Substitute 30x+4 for MC¯ in above equation and evaluate by the use of the integral formula xndx=< (b) To determine To calculate: The number of units that will result in maximum profit if the marginal revenue for a product is MR¯=900 and marginal cost of the product is MC¯=30x+4 and fixed cost is$1,000.

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