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Sloan [31]
3 years ago
10

A company sells widgets. The amount of profit, y, made by the company, is related to

Mathematics
1 answer:
just olya [345]3 years ago
7 0

Answer:

$978

Step-by-step explanation:

Given:

  • y = amount of profit
  • x = selling price of each widget
  • y=-x^2+78x-543

To find the maximum amount of profit, differentiate the equation, set it to zero and solve for x.  Substitute found value of x into the original equation.

<u>Differentiate equation</u>

       y=-x^2+78x-543

\implies \dfrac{dy}{dx}=-2x+78

<u>Set differentiated equation to zero and solve for x</u>:

      \dfrac{dy}{dx}=0

\implies -2x+78=0

\implies 2x=78

\implies x=39

<u>Maximum profit</u>

Substitute x = 39 into the equation:

\implies -(39)^2+78(39)-543=978

Therefore, max profit is $978

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Step-by-step explanation:

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Step-by-step explanation:

Given

Length of rectangle is 6\ ft

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