Question

Cycle Accessories manufacturers cellphone holders that can be mounted on the handle bars of most motorcycles. The manufacturing process is highly automated and management feels that machine-hours are likely the main driver of overhead costs. Data from the most recent year are shown below.

Month	Machine-Hours	Overhead Costs
January	3,100	$	59,600
February	3,160		63,620
March	3,400		70,400
April	4,120		77,120
May	4,300		78,960
June	4,900		78,480
July	5,500		88,320
August	6,100		88,070
September	5,800		84,880
October	4,300		77,120
November	3,460		72,000
December	5,500		85,200

Required:

1. Using least-squares regression, estimate the fixed cost and variable cost elements of monthly overhead costs. Estimate the fixed cost element to the nearest dollar and the variable cost element to the nearest cent.

Fixed cost
Variable cost		______ per machine hour

2. If the company expects to use 4,600 machine-hours next month, estimate total overhead costs.

Answer 1

Month	Machine Hours	Overhead costs	Machine Hours^2	Machine Hours*Overhead Costs
January	3100	59600	9610000	184760000
February	3160	63620	9985600	201039200
March	3400	70400	11560000	239360000
April	4120	77120	16974400	317734400
May	4300	78960	18490000	339528000
June	4900	78480	24010000	384552000
July	5500	88320	30250000	485760000
August	6100	88070	37210000	537227000
September	5800	84880	33640000	492304000
October	4300	77120	18490000	331616000
November	3460	72000	11971600	249120000
December	5500	85200	30250000	468600000
Total	53640	923770	252441600	4231600600

Unit Variable Cost (b) =	nΣxy − (Σx)(Σy)
	nΣx2 − (Σx)2
=	12*4231600600-(53640*923770)
=	12*252441600-(53640)^2
=	1228184400/152049600
=	8.08
Total Fixed Cost (a) =	Σy − bΣx
	n
=	(923770-8.08(53640))/12
=	40874	Per machine hour
b) Equation for overhead cost	y=a+bx
a	Fixed cost
b	Unit variable cost
x	Units produced
4600 Machine Hours=	40874+(8.08*4600)
	78042