Question

Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of it car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled: Month January February March April May June July August September October November December Rental Returns Car Wash Costs 2,500 $ 11,600 2,500 $ 13,400 2,800 $ 12,400 3,100 $ 15,200 3,700 $ 16,800 5,200 $ 24,500 5,600 $ 22,800 5,600 $ 23,700 4,800 $ 23,400 4,200 $ 22,900 2,300 $ 11,300 3,000 $ 16,300 2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. (Round Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.) Fixed cost per month Variable cost per rental return

Answer 1

	Month	Rental Returns(X)	Total Cost(Y)(in $)	Square of X	X*Y(in $)
	Jan	2,500	11,600	62,50,000	2,90,00,000
	Feb	2,500	13,400	62,50,000	3,35,00,000
	Mar	2,800	12,400	78,40,000	3,47,20,000
	Apr	3,100	15,200	96,10,000	4,71,20,000
	May	3,700	16,800	1,36,90,000	6,21,60,000
	Jun	5,200	24,500	2,70,40,000	12,74,00,000
	Jul	5,600	22,800	3,13,60,000	12,76,80,000
	Aug	5,600	23,700	3,13,60,000	13,27,20,000
	Sep	4,800	23,400	2,30,40,000	11,23,20,000
	Oct	4,200	22,900	1,76,40,000	9,61,80,000
	Nov	2,300	11,300	52,90,000	2,59,90,000
	Dec	3,000	16,300	90,00,000	4,89,00,000
	Total	45,300	2,14,300	18,83,70,000	87,76,90,000
		Unit Variable Cost (b) = nΣxy − (Σx)(Σy) /nΣx^2 − (Σx)^2		Total Fixed Cost (a) = Σy − bΣx / n
	So here n =12 ,Σx =45,300, Σy =214300, Σx^2=18,83,70,000 ,Σxy =87,76,90,000
	Variable cost per unit(b) =12*87,76,90,000 - (45,300*214,300) / 12*18,83,70,000 - 45,300^2
	Variable cost per unit(b) =10,53,22,80,000 - 9,70,77,90,000 / 2,26,04,40,000 - 2,05,20,90,000
	Variable cost per unit(b) =82,44,90,000 / 20,83,50,000 =$3.96
	Total Fixed cost =214,300 - ($3.96*45,300) / 12
	Total Fixed cost =(214,300 - 179,388) / 12
	Total Fixed cost =$34,912 /12 =$2,909