Question

What is the crossover point in miles between the hybrid vehicle and the alternative vehicle from a competing auto manufacturer? $19,500 $0.08 Hybrid Vehicle Vehicle Purchase Cost Vehicle Operating Cost per Mile Useful Life of Vehicle Miles per Year Miles per Gallon Average Fuel Price per Gallon $18,000 $0.14 14 years 15,000 33 $3.77 Alternative Vehicle Vehicle Purchase Cost Vehicle Operating cost per Mile Useful Life of Vehicle Miles per Year Miles per Gallon Average Fuel Price per Gallon 14 years 15,000 36 $3.77 The crossover point, M, is miles (round your response to the nearest whole number).

Answer 1

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To find the crossover point, we need to equate the total cost of both vehicles and solve for the total number of miles M.

Total Cost = Purchase Cost + [(Average Fuel Price per Gallon/ Miles per Gallon) + Vehicle Operating Cost per Mile] * (M Miles)

For hybrid vehicle, above expression becomes

Total Cost = 18000+[(3.77/33)+0.14]*M = 18000+0.254242M

For Alternative vehicle it becomes

Total Cost = 19500+[(3.77/36)+0.08]*M = 19500+0.184722M

To find the crossover point, we equate the above 2 and solve for M. Hence we have the below

19500+0.184722m=18000+0.254242m

Step 1: Simplify both sides of the equation.

0.184722m+19500=0.254242m+18000

Step 2: Subtract 0.254242m from both sides.

0.184722m+19500−0.254242m=0.254242m+18000−0.254242m

−0.06952m+19500=18000

Step 3: Subtract 19500 from both sides.

−0.06952m+19500−19500=18000−19500

−0.06952m=−1500

Step 4: Divide both sides by -0.06952.

−0.06952m

−0.06952

=

−1500

−0.06952

M = 21576.524741

Hence the crossover point is 21577 miles.