# Math Help - marginal cost

1. ## marginal cost

A manufacturer of small glass figurines discovers that it cost $2900 for a production run of 1300 and$3200 for a production run of 1700. Assuming that cost is a linear function of the number of items, find the overhead and the marginal cost of a figurine.

2. One neat way of doing this is to create an equation which looks like this:

total cost = (volume produced x unit cost) + overhead cost.

Then plug in the numbers for the volume produced and total cost from the question. You'll then have two equations that can be solved to find the unknowns that you need.

3. Thanks so much!

4. Originally Posted by littleone

A manufacturer of small glass figurines discovers that it cost $2900 for a production run of 1300 and$3200 for a production run of 1700. Assuming that cost is a linear function of the number of items, find the overhead and the marginal cost of a figurine.

"It cost $2900 for a production run of 1300" tells you that when N= 1300, C= 2900: 2900= A(1300)+ B. "and$3200 for a production run of 1700" tells you that when N= 1700, C= 3200: 3200= A(1700)+ B
Notice that even if N= 0, C= (3/4)(0)+ 1625= 1625 so even if we produce none at all, the cost is $1625. That is the overhead. If we produce only 1 item, the cost is (3/4)(1)+ 1625=$1625.75, $0.75 more. If we produce 2 items, the cost is (3/4)(2)+ 1625=$1626.50, $0.75 more than producing only 1. Do you see that every time we produce one more item, it will cost$3/4= \$0.75 more? That is the "marginal cost".