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Question
The Average Cost function associated with producing and marketing x units of an item is given by AC = `x + 5 + 36/x`.
- Find the Total cost function.
- Find the range of values of x for which Average Cost is increasing.
Solution
Give, AC(x) = `x + 5 + 36/x`
a. T.C(x) = x × AC
= `x(x + 5 + 36/x)`
= x2 + 5x + 36
b. Given, AC = `x + 5 + 36/x`
`d/dx(AC) = 1 - 36/x^2`
AC increases, when `d/dx(AC) > 0`
`\implies 1 - 36/x^2 > 0`
`\implies 1 > 36/x^2`
`\implies` x2 > 36
`\implies` x2 – 36 > 0
`\implies` (x – 6)(x + 6) > 0
`\implies` x > 6 or x < – 6
As x is positive, AC increases when x > 6
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