Find The Maximum Profit That A Company Can Make If The Profit Function Is Given By p(x) = 41 − 72x − 18x2.

Sol:

Given:

p(x) = 41 – 72x – 18x2

⇒ p(x) = 41 – 72x – 36x

By adding this equal to zero, we get x = −2

Now let’s look at the second derivative of the given function.

f'(x) = -36 and as we can see, this is negative for all x; hence f(x) will have its maxima at x=−2.

The maximum profit which the company is going to make is

p(−2) = 41 – 72 * (−2) – 18 * (−22)

p(−2) = 41 – 72 * (−2) – 18 * (4)

p(−2) = 41 – (-144) – (72)

p(−2) = 113.

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