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[Step-by-Step] [Profit maximization - III] If the producer’s cost function is C(q)=(q^3)/(3)-7q^2+111q+50 and the demand function is q=100-p where p is

Question: [Profit maximization - III]

If the producer’s cost function is

\[C\left( q \right)=\frac{{{q}^{3}}}{3}-7{{q}^{2}}+111q+50\]

and the demand function is

\[q=100-p\]

where p is the selling price per unit.

  1. Write out the total revenue function R in terms of q.
  2. Write out the profit function \(\Pi \) in terms of q.
  3. Find the output quantity q* which leads to maximum profit.
  4. Compute the maximum profit.

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