Question

The total cost and the total revenue of a company that produces and sells x units of a particular
product are respectively.
Cx= 5x÷ 350 and Rx = 50x - x
ind ) the breakeven values
(2) the values of x that produces a profit
(5) the values of x that result in a loss​

Answer 1

Given :    The total cost and the total revenue of a company that produces and sells x units of particular product are respectively

C(x) = 5x + 350 and R(x) = 50x – x².

( correction in Question)

To Find :

(i) the breakeven values

(ii) the values of x that produce a profit

(iii) the values of x that result in a loss.

Solution:

C(x) = 5x + 350

R(x) = 50x – x²

breakeven  

C(x) = R(x)

=>  5x + 350  = 50x – x²

=> x² - 45x + 350 = 0

=> (x - 10)(x - 35) = 0

=> x = 10 , 35

breakeven values are 10 and 35 units

x that produces a profit

R(x) - C(x) > 0

50x – x² - 5x - 350 >  0

=> -x² + 45x - 350  > 0

=> x² - 45x + 350 < 0

=> (x - 10)(x - 35) < 0

      10 < x  < 35

10 < x  < 35  produces a profit

values of x that result in a loss​

0<  x  < 10  and  35 < x

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