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.

page revision: 9, last edited: 02 Jun 2011 22:39