A small business owner has determined that the cost to produce 15 desks in a month is $16,000 and the cost to produce 25 desks in a month is $24,750.

Question

1. Find a formula linear function that models the number of desks produced in a month, C, if the number of desks produced is n.

Answer 1

think of it as two points (15, 16) and (25, 24.75)

then find the line that goes through those 2 points. It has slope = (24.75-16)/(25-15) = 8.75/10

C=(.875)D + b where b is the y or C intercept

plug in either point to solve for b

16 = .875(15) + b

b = 16 - 13.125 = 2.875

C = (.875)D + 2.875 in units of a thousand dollars

Total Cost = variable cost of $875 x number of desks + fixed cost of $2,875