The cost, C, of a manufacturing and selling x units of a product is C = 23x+73, and the corresponding revenue, R, is= x^2-35. Find the break-even value of x?
A. 4
B. 31
C. 31 and 4
D. 27
Break-even point: C = R
23x + 73 = x^2 - 35
Set equation equal to 0:
0 = x^2 - 23x - 108
Try to factor:
0 = (x - 27)(x + 4)
Set each factor equal to 0:
x - 27 = 0
x + 4 = 0
Possible solutions: -4, 27
Throw out the negative number and you will have your answer!
I hope this helps.
To find the break-even value of x, we need to determine the value of x when the cost (C) equals the revenue (R).
The cost equation is given by C = 23x + 73.
The revenue equation is given by R = x^2 - 35.
Setting C equal to R, we have:
23x + 73 = x^2 - 35
To solve this equation, we can rearrange it into a quadratic equation:
x^2 - 23x - 108 = 0
Next, we can factor this quadratic equation or use the quadratic formula to find the roots. Since we are looking for a positive value of x, we can omit the negative root.
Factoring the equation, we have:
(x - 31)(x + 4) = 0
Setting each factor equal to zero and solving for x, we get:
x - 31 = 0 (x = 31)
x + 4 = 0 (x = -4)
Since we are looking for a positive value of x, the break-even value is x = 31.
Therefore, the answer is B. 31.