#### Answer

105 units

#### Work Step by Step

C(x)=x^2-15x+50
C(x)=9500
9500=x^2-15x+50
x^2-15x+50-9500
Simplify
x^2-15x-9450
Using ac method a=9450 b=-15
Find two numbers whose products are 9450 and whose sums are -15.
The two numbers are -105 and 90 so rewrite
x^2-105x+90x-9450=0
x(x-105)+90(x-105)
(x+90)(x-105)=0
x+90=0 x=-90
x-105=0 x=105
Since the answer can't be negative then production of 105 units would cost $9500.
C(x)= (105)^2-15(105)+50
C(x)= 9500