math problem need help

Question

A company manufactures small refrigerators. The total cost to manufacture 63 refrigerators is $10125. The total costs to manufacture 172 refrigerators is $24295. Assume that total cost, C, is linearly related to the number of refrigerators, x, the company manufactures and includes a fixed cost and a cost per refrigerator.

 B) The total cost to manufacture 177 refrigerators is $

D) The cost to produce each additional refrigerator is $

Answer 1

10125 = 63r + F

24295 = 172r + F where F=Fixed Costs and r= variable cost per refrigerator

fixed cost + variable cost = Total Cost=C

2 equations 2 unknowns

solve by elimination substitution or matrix algebra for r and F

subtract 1st equation from 2nd

14170 = 109r

r = 14170/109 = $130

F= 10125-63(130)= 10125-819= $9306 = Fixed cost

then

C(x)= xr+F

and

C(177) = 177r+F, just plug in the values for r and F

= 177(130)+ 9306= $32316 for 177

MC = Marginal Cost = cost of an additional refrigerator = C'(x) = (xr+F)' = r= $130