In Each Case Below, Find the Profit-Maximizing Level of Output $\pi$

question 17

Essay

In each case below, find the profit-maximizing level of output. Verify that each output level is a maximum by checking the second derivative.
(a) $\pi$ = -50 + 200Q - 10Q²
(b) π = –100 + 300Q – 4Q³

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Definitions:

Bank Loan

A sum of money lent by a bank to a borrower at a specified interest rate to be repaid with interest.

Partnership Debts

Obligations for which all partners are jointly responsible in a partnership setup, meaning each partner can be held accountable for the entire amount of the debt.

Initial Capital

The amount of money or assets used to start a business or investment.

Continuation Agreement

A legal contract that extends the period of a previous agreement, ensuring the ongoing provision of services or terms.