Question

Adam has just accepted a job in Alaska, where self-service gas stations are generally not available. Thus each trip to the gas station for his 1983 Chevette will entail a $3 tip to the gas station attendant for their services; we ignore any other cost that he incurs in order to drive to the gas station (e.g., the gas consumed to drive there). Gas costs $3.75 per gallon. Adam’s job is to deliver hot Italian food. By calculating his driving distance and his Chevette’s gas mileage, Adam anticipates that he needs to consume 105 gallons of fuel in a 7-day week. For cash not used for gas, Adam can do some investment and get a 6% daily return on average.

(4 points) Based on the EOQ method, how many gallons Adam should fuel up each time?

(2 points) Given the above fueling quantity, how much money does Adam need to tip per week, on average?

2 points) If Adam’s Chevette tank can hold 12 gallons of gas at most, how many times each week should he fuel on average?

Answer 1

Part A:

Economic order quantity concept- Mainly used in production engineering setup. The objective of EOQ is to optimize the cost of inventory. The formula for EOQ is -

Order Quantity = ((Annual demand * Fixed cost per order)/ annual holding cost per unit)^(1/2)

-Here our order quantity becomes the gallons Adam should fuel up each time

-Weekly demand - 105 gallons

-Each unit fixed cost- $3.75

-Holding cost (opportunity cost per visit/unit) - $3

EOQ - ((105*3.75)/3)^(1/2) = (393.75/3)^(1/2)= (131.25)^(1/2) = 11.45644 Gallons/ time

Part B:

The total money required as a tip in a week = (No of visit*Per time tip amount)

No. of visit = Total required fuel / optimal quantity for each trip

= (105/11.45644) = 9.16

No. of trips cannot be in fraction hence take upper celling number so total 10 trips are required in every week

The total money required as a tip in a week = (No of visit*Per time tip amount)

= 10 * $3 = $30

Part C:

Total no. of trip required = Fuel required in 7 days/ Max fuelling at each trip

= 105/12= 8.75 Which means 9 trips each month