The formula for the total cost of producing an item is C=8x^2-176x+1800, where x is the
number of units that the company makes.
To minimize the cost of manufacturing, the company should produce a number of items.
Determine this number.
Solution
We notice that the formula for the total cost is a function which is depending on the number of
items manufactured.
To find the minimum value for the cost, we have to differentiate the cost function.
C'(x) = (8x^2-176x+1800)'
C'(x) = 16x - 176
From the theory, we know that a function has an extreme point, where it's first derivative is
cancelling.
C'(x) = 0
16x - 176 = 0
16x=176
x=176/16
x=11
To verify if the point is a maximum or a minimum,we have to differentiate twice C(x).
C"(x) = (16x - 176)'
C"(x) = 16>0
That means that any critical value will be a minimum.
So, to minimize the cost, the number of items should be x=11.