Question

George Caloz & Frères, located in Grenchen, Switzerland, makes prestige high-end custom watches in small lots. One of the company’s products, a platinum diving watch, goes through an etching process. The company has observed etching costs as follows over the last six weeks:

Week	Units			Total Etching Cost
1		10		$	27
2		7		$	20
3		12		$	31
4		6		$	20
5		8		$	24
6		11		$	30
		54		$	152

For planning purposes, management would like to know the amount of variable etching cost
per unit and the total fixed etching cost per week.

Required:

2(a). Using the least-squares regression method, estimate the variable and fixed elements of etching cost. (Round your answers to 2 decimal places.)

     

2(b). Express the cost data in (2a) above in the form Y = a + bX. (Round your answers to 2 decimal places.)

     

3. If the company processes nine units next week, what would be the expected total etching cost? (Round your intermediate and final answers to 2 decimal places.)

Answer 1

2-a	Assessment of the variable and fixed cost elements of etching costs by least square regression methods
	by the equation
		Y	a+bX
		Where X=Number of etching cost per unit
		a=Fixed Cost
		b-Variable Cost
	Calculation of the a and b in the following format
	Week	Units-X	Total Etching Cost-Y	XY	X^2
	1	10	27	270	100
	2	7	20	140	49
	3	12	31	372	144
	4	6	20	120	36
	5	8	24	192	64
	6	11	30	330	121
	Total	∑X=54	∑Y=152	∑XY=1424	∑X^2=514
	Σy is the sum of total costs,
	Σx is the sum of units,
	Σxy is the sum of the products of cost and units,
	Σx2 is the sum of squares of units of all data pairs.
	N is 6 weeks.
	b	n∑xy-∑x∑y/n(∑x^2)-(∑x)^2
		6*1424-54*152/(6*514)-(54*54)
		2
	Fixed Cost
	a	152-(2*54)/6
		134
b	Calculation of cost data in (2a) above in the form
	Y = a + bX
	Y = 134 + 2 X.
3	If the company processes nine units next week, what would be the expected total etching cost?
	By the equation we get
	Y	134+2X
	Here	X=9
	There fore putting X in the following equation we get the value of Y expected in the next week as below:
	Y	134+2*9
		152