Question

Problem 3: If annual operating costs (AOC) for ABC company is as follows: Days AOC 320 260 315 $200,000 $138,000 $160,000 $140,000 $155,000 280 310 A. Use Least Square Method to separate the AOC into fixed and variable costs. B. Estimate the AOC if the number of working days in the next year is 290.

Answer 1

a) Slope of the line = m

Equation of the line, Y = mX + b

	Days(X)	AOC(Y)	X^2	XY
	320	200000	102400	64000000
	260	138000	67600	35880000
	315	160000	99225	50400000
	280	140000	78400	39200000
	310	155000	96100	48050000
Total	A = 1485	B = 793000	C = 443725	D = 237530000

m = [(N*D) - (A*B)] / [(N*C) - A^2]

where A,B,C,D are classified above in the table while N is the number of observations which is 5.

m = [(5*237530000) - (1485*793000)] / [(5*443725) - 1485^2] = 749.62

b = (B - m * A) / N = (793000 - 749.62*1485) / 5 = -64039.18

Fixed cost is the cost which is always there even if zero units is produced. Thus fixed cost is,

Y = 749.62*0 - 64039.18 = -64039.18

b) y = mx + b

y = 749.62 * 290 - 64039.18 = 153352.61