Question

Let LaTeX: C(x)C ( x ) be the cost in dollar of manufacturing x items. If we are given that C(10)=101 and C'(10) = 3 then estimate the cost to manufacture 12 items

Answer 1

We have C(10)=$101 which is the cost C(x) at the production level x=10 units. The derivative of the cost function is the marginal cost which is written as C'(x).

Marginal cost is defined as cost of producing one additional unit when the production level is at x. Here marginal cost at production level x=10 is given as C'(10)=3. Therefore we can say that the cost of producing one additional unit when the current production level x=10 is $3.

So, we can write the cost of producing 11 units as $101+$3=$104

We cannot accurately predict the cost of producing 12 items because marginal cost at x=11 units is not given. If we assume the marginal cost remains almost constant then we can approximate the cost of producing 12 items as

C(12)=101+2*(3)=107

So, the cost of producing 12 items will be approximately $107