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The profit in manufacturing x refrigerators per day, is given by the profit relation p = ¡3x2 + 240x ¡ 800 dollars. a how many refrigerators should be made each day to maximise the total profit? b what is the maximum profit?

Respuesta :

merlynthewhizz
The given equation is -3x²+240x-800

The maximum of the function is given when [tex]x=- \frac{b}{2a} [/tex] where a and b are the constant of a quadratic form ax²+bx+c

We then have
a = -3
b = 240

Substitute these values into the maximum/minimum formula we have
[tex]x= \frac{-240}{2(-3)} = \frac{240}{6}=40 [/tex]

Which means that the maximum profit is obtained when the number of refrigerators produced is 40 items a day

The maximum profit is 

p = -3(40)²+240(40)-800 = $4000




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