Question

The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their​ long-haul tractors. Three types of​ deflectors, with the following​ characteristics, are being considered ​(MARRequals=99​% per​ year): Windshear Blowby ​Air-vantage Capital investment ​$700700 ​$500500 ​$1 comma 3001,300 Drag reduction 1616​% 88​% 2424​% Maintenance per year ​$1111 ​$55 ​$44 Useful life 99 years 1212 years 55 years If 44​% in drag reduction means 33​% in fuel savings per​ mile, how many miles do the tractors have to be driven per year before the windshear deflector is favored over the other​ deflectors? Over what range of miles driven per year is​ air-vantage the best​ choice? (Note: Fuel cost is expected to be ​$3.003.00 per​ gallon, and average fuel consumption is 55 miles per gallon without the​ deflectors.)

Answer 1

Answer:

The annual operating expenses of long-haul tractors equipped with the various deflectors are calculated as a function of mileage dirven per year, X

Annual Operating Expenses= X miles/Year x Possibility with drag reduction x fuel savings x $3 per gallon

Possibility with Drag reduction

Windshear = 1-(2%/5%) x 15% 0.94

Blowby = 1-(2%/5%) x 10% 0.96

Air Vantage = 1-(2%/5%) x 20% 0.92

Windshear: [(X miles/yr)(0.94)(0.25 gallon/miles)($3.00/gal)] = 0.705 x/yr

Blowby: [(X miles/yr)(0.96)(0.25 gallon/mile)($3.00/gal)] = 0.72 x/yr

Air-vantage: [(X mi/yr)(0.92)(0.25 gal/mi)($3.00/gal)] = 0.69 x/yr

EUAC can now be written in terms of X

EUAC Windshear =$800(A/P,12,%; 8) + $9 + $0.705X = $170.04 + $0.705X

EUAC Blowby =$500(A/P,12,%; 9) + $6 + $0.72X = $99.85 + $0.72X

EUAC Air Vantage =$1200(A/P,12,%; 6) + $6 + $0.69X = $297.84 + $0.69X

The breakeven values can be computed between each pair of deflectors by equating their EUAC equations and solving for X

Windshear and Blowby: = $170.04 + $0.705 x = $99.85 + $0.72X/yr $4,679.33 miles per year

Blowby and Air-vantage = $99.85 +$0.72x = $297.84 + 0.69X $6,599.67 miles per year

Air-vantage and Windshear = $297.84 +.69x =$170.04 +0.705x $8,520 miles per year

Determine the range over which each deflector is preferred

x< $4,679.33 select blowby

$4,679.33 <x< $8,520 select windshear

$8,520<x select air-vantage

Gallon per miles = 1/4 miles 0.25