SOLUTION: 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 decrea

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 maxamize profit?
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(21583) (Show Source):
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Answer by ankor@dixie-net.com(12692) (Show Source):
You can put this solution on YOUR website!
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 =
In this equation: a=-.1, b=60
x =
x = +300 units + the original 300 units = 600 units yield max profit