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Question
Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x2.
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Solution
We have p(x) = 41 − 72x − 18x2
p'(x) = −72 − 36x
Now for critical points, p’(x) = 0
−72 − 36x = 0
−72 = 36x
x = `36/(−72)`
x = −2
p”(x) = −36 < 0
∴ Profit is maximum at x = −2, and maximum profit is p(−2) = 41 − 72 (−2) − 18 (−2)2
= 41 + 144 − 72
= 185 − 72
= 113
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