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The owner of a fabric store has determined that the profits P of the store are approximately given by P(x) = -x^2 + 70x+67, where x is the yards of fabric sold daily. Find the maximum profit to the nearest dollar. a) $617 b) $792 c) $1017 d) $1292 e) none

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Answer: Option 'd' is correct.

Explanation:

Since we have given that

Profit function of the store is given by


P(x)=-x^2+70x+67

We need to find the maximum profit.

For this, we first derivate the above function:


P'(x)=-2x+70

Now, put P(x) = 0, we get that


-2x+70=0\\\\-2x=-70\\\\x=35

Now, we will check that its maximality by finding the second derivative:


P''(x)=-2<0

it gives maximum profit at x = 35 yards.

And the maximum profit would be


P(35)=-(35)^2+70* 35+67=\$1292

Hence, Option 'd' is correct.

User Juan Luis
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