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.)

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)] =0.705x/yr

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

Air-vantage: [(X mi/yr)(0.92)(0.25 gal/mi)($3.00/gal)] =0.69x/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$4,679.33miles per year

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

Air-vantage and Windshear = $297.84 +.69x =$170.04 +0.705x$8,520miles 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 miles0.25

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