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# Calculus/Maximum-minimum problem

Question
p=129-0.5x and total cost C=50x+32.75 , where x is the number of units. Find what price yields a maximize profit and when the profit is maximized, what is the average cost per unit?

Questioner:   Megan
Country:   Tennessee, United States
Category:   Calculus
Private:   No
Subject:   Basic calculus
Question:   p=129-0.5x and total cost C=50x+32.75 , where x is the number of units. Find what price yields a maximize profit and when the profit is maximized, what is the average cost per unit?
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I think you mean:

Find what value of x yields a maximum profit.

I think you left out:

Let the price function be designated as p.

Let the profit function be designated as P.

['P' is not the same as 'p'.]

Then P = price * x - cost.

P = x(129 - 0.5x) - 50x + 32.75

P = 129x - 0.5x^2 - 50x + 32.75

P =      - 0.5x^2 - 79x + 32.75

After that, the rest is routine.  Find x to maximize P:

Differentiate, set P' = 0, solve.

Then you can answer the other questions.  If you you get stuck, let me know.

Calculus

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#### Paul Klarreich

##### Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

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I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

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