Question

10-27 Estimating a cost function, high-low method. FlyHigh Vacations offers helicopter service from suburban towns to Heathrow Airport in the United Kingdom. Each of its 10 helicopters makes between 1,000 and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000 round-trips in the year incurs an average operating cost of $350 per round-trip, and one that has made 2,000 round-trips in the year incurs an average operating cost of $300 per round-trip. 1. Using the high-low method, estimate the linear relationship y = a + bX, where yis the total annual oper- ating cost of a helicopter and Xis the number of round-trips it makes to Heathrow Airport during the year. 2. Give examples of costs that would be included in a and in b. 3. If FlyHigh Vacations expects each helicopter to make, on average, 1,200 round-trips in the coming year, what should its estimated operating budget for the helicopter fleet be?

Answer 1

Here, since we are given the total average operating cost for helicopter, we will use this to generate the equation and would try to find the value of third party of the question.

1) Average cost of $350 if helicopter makes 1000 rounds. Total rounds done by 10 helicopter is 10,000. So total cost = $350*10000=$3500,000
so equation 1 is 3500,000=a+1000b

similarly, we will use the average cost of $300 if helicopter makes 2000 rounds.
so total cost =$300*10*2000=$6000,000

so equation 2 is 6000,000=a+2000b

we will subtract equation 2 with equation 1 to get the value is a and b

1000b=2500,000

b=2500

using value is b in equation 1, we will get

a=3500,000-2500*1000

a=1000,000

thus the equation will become Y = 1000,000 + 2500X

2) Costs included in a which is 1000,000 is the fixed cost that the company have to beat even if there are no rounds which can be general maintenance, administration cost, rental outflows and salaries of operators.

Costs that can be included in b which is incurred per round is the running costs that is Fuel costs, maintenance costs etc

3) Here, we will use the equation which we have derived in part 1) of the question

Y = 1000,000+2500X

Y= 1000,000 + 2500*1200

Y = 4000,000

this, annual operating cost of fleet of 10 helicopters that does 1200 rounds is $4000,000