# Calculus Cost Function

PROBLEM 1 : This case study is to be presented in the form of a report or at least provide reasons for the answers.

A computer manufacturing company has a fixed cost of \$3000 and a variable cost of 0.3𝑥² + 80𝑥 . The company needs to gather information to determine its cost function, the company then needs to derive the cost incurred for a production of 400 computers. Discuss and make interpretations on the findings for each additional computer purchased at a production level of 400 and find the exact cost to produce the 401st computer. Managers then need to evaluate the profitability of a new product using the equation p = 200-0.005x. Determine the revenue function and the number of units required to maximize revenue. Discuss and make interpretations, on this new product for the company’s next meeting.

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PROBLEM 2 :

A company hires you to provide financial advice, they provide the marginal cost function and the

marginal revenue function.

C’ (x) = 0.3𝑥² + 20x

R’ (x) = 120x

• Compute the marginal profit function. Given that the fixed cost is \$5000, find:

• The cost function C(x)

• The revenue function R(x)

• Determine the breakeven point (illustrations can be used) and discuss the findings based on these values. Discuss how the company should move forward to improve their business.

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