Question

Developing an Equation from Average Costs The America Dog and Cat Hotel is a pet hotel located in Las Vegas. Assume that in March, when dog-days (occupancy) were at an annual low of 500, the average cost per dog-day was $14. In July, when dog-days were at a capacity level of 4,000, the average cost per dog-day was $7. (a) Develop an equation for monthly operating costs. (Let X = dog-days per month) Total cost = Answer + Answer * X (b) Determine the average cost per dog-day at an annual volume of 24,000 dog-days.

Answer 1

Answer

• The problem can be addressed by the use of High Low Method to find Variable cost per dog days (units) and Fixed cost.
• Workings

	Units	Cost
High Level	4,000	$                   28,000.00 [4000 x $ 7]
Low Level	500	$                     7,000.00 [ 500 x $ 14]
Difference	3,500	$                   21,000.00

A	Difference in Cost		$                   21,000.00
B	Difference in units		3,500
C = A/B	Variable cost per unit		$                             6.00
Working		High Level	Low Level
A	Total Cost	$                 28,000.00	$                     7,000.00
B	Total Units	4000	500
C	Variable cost per unit	$                           6.00	$                             6.00
D = B x C	Total Variable cost	$                 24,000.00	$                     3,000.00
E = A - D	Total Fixed Cost	$                   4,000.00	$                     4,000.00

• Requirement [a]

Variable cost = $ 6 per dog day
Fixed Cost = $ 4000

Equation:
Total Cost = $ 4,000 + $ 6 * X

• Requirement [b]

Total Cost = $ 4,000 + $ 6 * X

Total Cost = 4000 + ($6 x 24000 dog days)
= 4000 + 144000
= $ 148,000 = Answer