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A company sells widgets. The amount of profit, y, made by the company, is
related to the selling price of each widget, x, by the given equation. Using this
equation, find out what price the widgets should be sold for, to the nearest
cent, for the company to make the maximum profit.
y = -x2 + 51x – 201

Respuesta :

Answer:

449.25 units

Step-by-step explanation:

The amount of profit, y, made by the company, is  related to the selling price of each widget, x, by the given equation as follows :

[tex]y=-x^2+51x-201[/tex] ...(1)

For maximum profit,

Put dy/dx = 0So,

[tex]\dfrac{d}{dx}(-x^2+51x-201)=0\\\\-2x+51=0\\\\x=\dfrac{51}{2}\\\\x=25.5[/tex]

Now put x = 25.5 in equation (1).

[tex]y=-(25.5)^2+51(25.5)-201\\\\y=\$ 449.25[/tex]

so, the required answer is 449.25 units.