8. A profit making company wants to launch a new product. It observes that fixed cost of
the new product is 35000 and the variable cost per unit is 500. The revenue function
for the sale of x units is given by 5000x - 100x^2
Find the :
(i) profit function
(ii) breakeven values, and
(iii) the values of x that result in a loss.
Answers
Given : A profit making company wants to launch a new product. It observes that fixed cost of
the new product is 35000 and the variable cost per unit is 500. The revenue function
for the sale of x units is given by 5000x - 100x^2
To Find : (i) profit function
(ii) breakeven values, and
(iii) the values of x that result in a loss.
Solution:
fixed cost of the new product is 35000
variable cost per unit is 500
x = units produced
C(x) = Cost Function
C(x) = 35000 + 500x
R(x) = 5000x - 100x²
Profit Function P(x)
P(x) = R(x) - C(x)
=> P(x) = 5000x - 100x² - ( 35000 + 500x)
=> P(x) = 4500x - 100x² - 35000
breakeven values
C(x) = R(x) or P(x) = 0
4500x - 100x² - 35000 = 0
=> x² - 45x + 350 = 0
=> (x - 35)(x - 10) = 0
=> x = 35 , x = 10
Breakeven is on 10 unit
Profit is between 10 and 35 unit
values of x that result in a loss.
x < 10 and x > 35
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