# What is the total cost (in dollars) of producing x golf clubs per day is given by the formula C(x)=400+100x−0.7x2 ? (A) Find the marginal cost at a production level of x golf clubs. (B) Find the marginal cost of producing 20 golf clubs.

Jun 26, 2018

$C \left(1\right) - C \left(0\right) = 99.30$
$C \left(21\right) - C \left(20\right) = 71.30$
Where your real margin is depends on the available selling price.

#### Explanation:

The marginal cost of production is the change in total cost that comes from making or producing one additional item. The purpose of analyzing marginal cost is to determine at what point an organization can achieve economies of scale.
https://www.investopedia.com/terms/m/marginalcostofproduction.asp
From the expression for the cost of production:
C(x) = 400 + 100x − 0.7x^2
the "increment" of one club is:
C(1) - C(0) = [400 + 100(1) − 0.7(1)^2] - 400 = 99.3

To produce 20 clubs this becomes
C(20) = 400 + 100(20) − 0.7(20)^2 = 2120
vs.
C(21) = 400 + 100(21) − 0.7(21)^2 = 2191.3

or $2191.3 - 2120 = 71.3$