Hello! Will someone please help me?
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.
Thanks in advance.
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.
Do you know what those words mean? If you do, this is easy. If not, it is impossible!
Originally Posted by littleone
"Assuming cost is a linear function of the number of items" means it is a function of the type C= AN+ B where C is the "cost", N is the "number of items" and A and B are constants you need to determine. You can do that by putting in the values of C and N you are given.
"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
Now subtract the first of those two equations from the second: 3200- 2900= A(1700- 1300)+ B- B. "B- B= 0" so we have eliminated B from the equation. What we have left is 3200- 2900= 300= 400A. A= 300/400= 3/4.
Going back to 2900= A(1700)+ B and using 3/4 for A, 2900= (3/4)(1700)+ B= 1275+ B so B= 2900- 1275= 1625.
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".