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Question
Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x2, where x is the number of units and P is the profit in rupees.
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Solution
For maxima and minima,
P'(x) = 0
`\implies` 42 – 2x = 0
`\implies` x = 21 and P"(x) = –2 < 0
So, P(x) is maximum at x = 21.
The maximum value of P(x) = 72 + (42 × 21) – (21)2 = 513
i.e., the maximum profit is ₹ 513.
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