Step-by-step explanation:
We can find the maximum profit by taking the derivative of the profit and then solving for the widget price x that will maximize it. It is done by equating the derivative to zero:
[tex]\dfrac{dy}{dx} = -12x + 600 = 0[/tex]
Solving for x, we get
[tex]x = \dfrac{600}{12} = \$50[/tex]
By setting the widget price to $50, the company can maximize their profits. To find this maximum profit, substitute the value of x into the equation for the profit:
[tex]y = -6(50)^2 + 600(50) - 5726[/tex]
[tex]\;\;\;=\$9,274[/tex]
