Answer:
The number of units that must be produced to break even is 25.
Step-by-step explanation:
Given : The revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. [tex]R(x) = 200x-x^2[/tex] ; [tex]C(x) = 65x+2750[/tex] ; [tex]0 \leq x \leq100[/tex]
To find : The number of units that must be produced to break even ?
Solution :
We know that,
At break even the cost price and revenue became equal.
So, [tex]C(x)=R(x)[/tex]
Substitute the values,
[tex]65x+2750=200x-x^2[/tex]
[tex]65x-200x+x^2+2750=0[/tex]
[tex]x^2-135x+2750=0[/tex]
Applying middle term split,
[tex]x^2-110x-25x+2750=0[/tex]
[tex]x(x-110)-25(x-110)=0[/tex]
[tex](x-110)(x-25)=0[/tex]
Either x=110 or x=25
Since, [tex]0 \leq x \leq100[/tex]
The value of x is 25.
Therefore, the number of units that must be produced to break even is 25.
