Question

A company sells widgets. The amount of profit, y, made by the company, is related tothe selling price of each widget, x, by the given equation. Using this equation, find outwhat price the widgets should be sold for, to the nearest cent, for the company tomake the maximum profit.y=-302+ 1325. – 8569

Answer 1

Step 1

Choose a method to solve the quadratic equation and state it

For this problem, we will differentiate the given equation to find the maximum value

`\begin{gathered} y\text{ = }-30x^2+1325x\text{ -856}9 \\ (dy)/(dx)=2(-30)x^(2-1)+(1)(1325)x^(1-1)^{}^{}_{}-8569 \\ (dy)/(dx)=-60x\text{ + 1325 } \end{gathered}`

Step 2

find the value of x, knowing that at the maximum point of the profit the equation we got after differentiation = 0

`\begin{gathered} -60x\text{ +1325 = 0} \\ -60x\text{ = -1325} \\ (-60x)/(-60)=(-1325)/(-60) \\ x\text{ =\$22.03333}\ldots\ldots\ldots\ldots.. \end{gathered}`

To the nearest cent, the price of one widget for maximum profit is $22.03