Maximizing Profit: Finding Marginal Cost, Revenue, and Integration, Exams of Calculus

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Total Cost and Profit

Gina Rablau

Gina Rablau

1

Total Cost and Profit

A Mini Project for Module 1

Project Description

This project demonstrates the following concepts in integral calculus:

Indefinite integrals.

Project Description

Use integration to find total cost functions from information involving marginal cost (that is, the rate of change of cost) for a commodity.
Use integration to derive profit functions from the marginal revenue functions.
Optimize profit, given information regarding marginal cost and marginal revenue functions.

The marginal cost for a commodity is M C = C′(x), where C(x) is the total cost function. Thus if we have the marginal cost function, we can integrate to find the total cost. That is, C(x) =ᔖ ᠹᠩ ᡖᡶ.

The marginal revenue for a commodity is M R = R′(x), where R(x) is the total revenue function.

If, for example, the marginal cost is MC = 1.01(x + 190)0.01^ and

M R = ( 1 / 2 x + 1 ) + 2 , where x is the number of thousands of units and both revenue and

cost are in thousands of dollars. Suppose further that fixed costs are $100,236 and that production is limited to at most 180 thousand units.

C ( x )= (^) ∫ MCdx =∫1.01(x+190)0.01^ dx = ( x+ 190 )^1.^01 + K