Brian's Delivery Service

Optimal Rate/Pace Example Problem

Brian has a delivery service with an odd fleet of five different vehicles. On a particular day he has five deliveries to make and needs to decide which vehicle to use for each delivery. Gas is $4.00/gallon. Help Brian decide which vehicle to use for each delivery.

Vehicle Fuel Efficiency (mpg) Cost per mile
Suburban 10 $0.40
Limousine 12 $0.33
Semi 6 $0.67
Prius 50 $0.08
Taurus 30 $0.13
Delivery Revenue Mile Traveled Revenue per Mile
A $20 35 $0.57
B $15 30 $0.50
C $12 22 $0.55
D $14 17 $0.82
E $8 15 $0.53

Rank each automobile cost per mile from lowest to highest and each delivery price (revenue) from highest to lowest.

Vehicle Cost/mi. Delivery Revenue/mi.
1 Prius $0.08 D $0.82
2 Taurus $0.13 A $0.57
3 Limo $0.33 C $0.55
4 Suburban $0.40 E $0.53
5 Semi $0.67 B $0.50

Match each vehicle with its associated delivery until Brian no longer makes a profit.

Combination Profit/mi. Total Profit
Prius + D $0.74 $12.58
Taurus + A $0.44 $15.40
Limo + C $0.22 $4.84
Suburban + E $0.13 $1.95
Semi + B $(0.17) ($5.10)

Answer: Use the Prius, Taurus, Limo, and Suburban to make deliveries D, A, C, and E respectively and wait until the Prius returns to make delivery B.

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