The Universal Postal Service is considering the possibility of fixing wind defle

Question

The Universal Postal Service is considering the possibility of fixing wind deflectors on the tops of 500 of their long haul tractors year) Three ypes of deflectors, with the follow ng character cs, are being considered MARR = 10% p Windshear Blowby S400 9% $4 12 years Air-vantage Capital investment Drag reduction Maintenance per year Useful life $800 12% S10 12 years $1,200 18% 56 6 years 113% in drag reduction means 2% in fuel air-vantage the best choice? (Note: Fuel cost is expected to be $2.75 per gallon, and average fuel consumption is 5 miles per gallon without the deflectors.) savings per mile, how many miles do the tractors have to be driven p er year before the windshear deflector is favored over the other deflectors? Over what range of miles driven per year is Click the icon to view the interest and annuity table for discrete compounding when the MARR is 10% per year Determine the range over which each deflector is preferred. (Round to the nearest hundreds) Select Blowby

Explanation / Answer

Assuming Repeatability of the deflector that it will be used continuously.

The annual operating expenses of long haul tractors equipped with the various deflectors are calculated as a function of mileage driven per year.

Let X be the mileage driven per year,then

Windshear: Total 8% reduction in fuel,Operating cost/year :

-(X/5)(0.92)(2.75) = -0.506 X/year

AW = -800(A/P,10%,12) -10-0.506 X

= -800(.1468) -10-0.506X

= -127.44 -0.506X

Blowby: Total 6% reduction in fuel,operating cost per/year:

-(X/5)(0.94)(2.75) = -0.517 X/year

AW = -400(A/P,10%,12) -4 -0.517X

= -62.72-0.517X

Air vantage: Total 12% reduction in fuel,operating cost/year:

-(X/5)(0.88)(2.75) = -0.484X/year

AW = -1200(A/P,10%,6) -6-0.484X

= -1200(.2296)-6-0.484X

= -281.52 -0.484X

BREAKEVEN POINTS

Windshear vs Blowby deflector:

-127.44-0.506X = -62.72-0.517X

X= 64.72/0.011 = 5883.6 miles per year

Windshear vs Air vantage Deflector:

-127.44-0.506X = -281.52-0.484X

X= 154.08/0.022 = 7003.6 miles per year

Blowby vs Air vantage Deflector:

-62.72-0.517X = -281.52-0.484X

X= 218.8/0.033 = 6630.3 miles per year

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