Question

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?

Answer 1

The given equation is -3x²+240x-800

The maximum of the function is given when $x=- \frac{b}{2a}$ 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
$x= \frac{-240}{2(-3)} = \frac{240}{6}=40$

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