Calculus/calculus

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Question
if the cost function of a commodity is c(x)=4x+10 and the ruvenue function is R(x)=16x-2x^2, where x is the number of units produces (in hundreds) and R(x) and C(x) are measured in thousands of pesos, find the ff.

1. profit function
2. most profitable output
3. maximum profitmost
4. revenue at the most profitable output
5. marginal revenue at the most profitable output
6. cost at the most profitable output

Answer
Given: cost C(x) = 4x + 10 and revenue R(x) = -2x + 16x.

1. Since profit P(x) = R(x) - C(x), we know P(x) = -2x + 20x + 10.

2. The most profitable output can be found when P'(x) = 0.
Since P'(x) = -4x + 20, putting this to 0 yields x = 5.

3. What is, 'profitmost'?  It sounds like the last question.

4. The revenue R(x) at the most profitable output of x=5 would be R(5).

5. The marginal revenue is found by finding R'(x) and putting in 5 for x.

6. The cost C(x) at the most profitable output is found by finding C(5).  

Calculus

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