Question

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even C(x)=16x+36,000 and R(x)=18x

Answer 1

Consider these specific values of x.

For example, if x=10, then C(10)=16(10)+36,000=160+36,000=36,160 (say $)

and R(10)=18*10=180.


So if only 10 units are produced, the total cost is 36,160, while the revenue is only 180 (again, say $.)



If, for example, x=1000, then we can calculate

C(1000)=16*1000+36,000=16,000+36,000=52,000

and

R(1000)=18*1000=18,000.


This suggests that with higher values of x, we can get to a particular point where the Cost and Revenue are the same. To find this point, we set the equation:
C(x)=R(x),

which gives us that particular x at which both C(x) and R(x) give the same value.

Thus, we solve 16x+36,000=18x. Subtracting 16x from both sides 2x=36,000, then x = 36,000/2=18,000.



Answer: 18,000