Question

, provides nationwide passenger train service on 21,000 miles of routes. Selected operating data for fiscal 2014 are shown below. Month Fuel Expense Passengers Passenger Train Miles (000s) $20,700 $22,897 (000s) Miles (000s) (000s) 475,187 465,902 375,339 380,750 481,458 475,037 499,435 498,117 550,741 579,939 507,644 496,599 October 2013 2,329 2,398 2,320 2,159 2,132 2,390 2,343 2,316 2,387 2,414 2,698 2,176 3,210 3,259 3,261 3,210 2,556 3,187 3,288 3,265 3,236 3,219 3,407 3,266 November 2013 December 2013 January 2014 February 2014 March 2014 April 2014 May 2014 une 2014 Duly 2014 August 2014 September 2014 $24,538 $22,225 $26,724 $25,853 $25,137 $25,034 $23,666 25,459 $25,331 The above data provide three possible activity measures that could influence fuel expense. Use the high-low method to develop a cost formula for fuel expense for each of the three measures. (Round unit cost to 2 decimal places,e.g.12.25 and fixed cost to nearest thousand dollars. Ir fixed cost is negat method enter amount with either negative sign preceeding the number, e.g9. -1,225 or parentheses, e.g. (1,225),) Passengers: Fuel expense x passenger Passenger miles: Fuel expense Train Miles Fuel expense x passenger mile x train mile

Answer 1

The answers are:

Passengers:
Fuel expense	=	$	5.71	*	passenger	+	$	10,043
Passenger miles:
Fuel expense	=	$	0.01	*	passenger mile	+	$	17,867
Train miles:
Fuel expense	=	$	3.80	*	train mile	+	$	12,512

Calculations:

(1): Passengers – Here the function is: y = a+bx where y = fuel expense, a = fixed costs and b = variable costs.

Variable cost = (y2-y1)/(x2-x1)

X2 = 2698 (highest no. of passengers) and y2 at this level (fuel expense) = 25459. X1 = 2132 (lowest no. of passengers) and y1 at this level = 22225

Thus variable cost = (25459-22225)/(2698-2132) = 5.71 per passenger.

Fixed cost (or a) = y2-bx2 = 25459 – (5.71*2698) = 10043.22

(2): Passenger miles – Here x2 = 579939 and y2 = 23666. X1 = 375339 and y1 = 21620

Thus variable cost = (23666-21620)/(579939-375339) = 0.01

Fixed cost = y2-bx2 = 23666-(0.01*579939) = 17866.61

(3): Train mile – x2 = 3407 and y2 = 25459. X1 = 2556 and y1 = 22225

Thus variable cost = (25459-22225)/(3407-2556) = 3.80

Fixed costs = y2-bx2 = 25459-(3.80*3407) = 12511.60