The minimum unit cost is $12,197.
Unit cost is given by the function is x^2-520x+79797.
Standard quadratic form is given by ax^2+bx+c
Comparing the given quadratic equation with standard quadratic form, we get
a = 1
b = -520
c = 79797
The minimum value occurs at the x coordinate -b/2a
Substitute the value of a and b,
-b/2a = -(-520)/2(1)
= 520/2
= 260
Substituting this value in the quadratic function:
C(x) = x^2-520x+79797
Now, C(260) = (260)^2 - 520(260)+ 79797
= 67,600 - 1,35,200 + 79,797
=$12,197
Hence, the minimum unit cost is $12,197
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