melly772
Answered

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Sagot :

Trancescient

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]

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