A company’s yearly total production cost C is typically given by C = C(n) = F + cn

Question

A company’s yearly total production cost C is typically given by C = C(n) = F + cn, where F is fixed cost and cn, the variable cost, is cost per item, c, times the number of items produced, n. If, in 2010, 1000 items were produced at a total cost of $3500 and, in 2015, 1500 items were produced at a total cost of $5000, determine the linear function C of n. What are the numerical values of F and c?

Answer 1

C = F +cn

3500 = F +100c

5000 = F + 1500c

subtract

1500 = 50c

c = 1500/50 = $30 cost per item

3500 = F +100(30)

F = 3500-3000= $500 fixed cost