Chapter 12.4, Problem 10E

### Mathematical Applications for the ...

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

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 cost for a product is M C ¯ = 60 x + 1 and its fixed cost is $340. If the marginal revenue for the product is M R ¯ = 80 x , find the profit or loss from production and sale of (a) 3 units. (b) 8 units. (a) To determine To calculate: The profit or loss from the production and sale of 3 units if the marginal revenue for a product is MR¯=80x and marginal cost of the product is MC¯=60x+1 and the fixed cost is$340.

Explanation

Given information:

The marginal revenue for a product is MR¯=80x and

Marginal cost of the product is MC¯=60x+1 and

The fixed cost is $340. 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¯=60x+1 And marginal revenue MR¯=80x Consider the formula of revenue function: R(x)=MR¯dx Substitute 80x for MR¯ in the equation R(x)=MR¯dx and evaluate by the use of the formula, xndx=xn+1n+1+K As, R(x)=80xdx=40x2 Consider the formula of cost function: C(x)=MC¯dx Substitute 60x+1 for MC¯ in above equation C(x)=MC¯ (b) To determine To calculate: The profit or loss from the production and sale of 8 units if the marginal revenue for a product is MR¯=80x and marginal cost of the product is MC¯=60x+1 and the fixed cost is$340.

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