Question 161826
A manufacturer finds that for the first 300 units of its product that are
 produced and sold, the profit is 60 dollars per unit. The profit on each of
 the units beyond 300 is decreased by $.10 times the number of additional units
 sold. What level of output will maximize profit?
:
Let x = no. of units produced over 300.
:
Total profit = Profit 1st 300 units + profit from additional x units
P = 300(60) + x(60-.1x)
P = 18000 + 60x - .1x^2
Arrange as a quadratic equation
P = .1x^2 + 60x + 18000
:
Find the level of max profit using the axis of symmetry formula: x = {{{(-b)/(2*a)}}}
In this equation: a=-.1, b=60
x = {{{(-60)/(2*-.1)}}}
x = +300 units + the original 300 units = 600 units yield max profit