Question

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

Answer 1

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.

Differentiate equation

       $y=-x^2+78x-543$

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

Set differentiated equation to zero and solve for x:

      $\dfrac{dy}{dx}=0$

$\implies -2x+78=0$

$\implies 2x=78$

$\implies x=39$

Maximum profit

Substitute x = 39 into the equation:

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

Therefore, max profit is $978