Project 1: Gas Station Problem

Work together in your groups to answer the following question. Pick one of your routes to school to work with. Discuss with your group members other considerations that will go into your decision-making process about going off of your route to get gas.

Let’s assume you drive to school every day. Map out your route and look at the gas stations that are on the way and how much the price of gas is at those stations. Then look at other gas stations in the area that are priced lower than the stations along your route. Would it be more economical for you to drive the extra distance for the less expensive gas than to purchase gas along your route? Would it be worthwhile for you to drive to the gas station that is priced lower than the others? Develop a mathematical equation that will determine your cost to get gas along your route and the cost to drive further away for cheaper gas to make your decision. Give your reasoning for those answers.

· Let p represent the price per gallon at the station along our route and P the price per gallon at the station we are considering.

· Let D represent the distance in miles from the normal route that must be driven to get to the gas station (so a round trip is 2D miles).

· Let M represent the miles per gallon of the vehicle.

· Let T represent the number of gallons of gas we purchase when we buy gas (in our model, four gallons less than the tank size).

Pick a route to school for one of the people in your group to use for this project. If everyone in your group lives on campus or out of the country, pick a location in Brevard County to use as “home” and map your route from that location. Pick one of your vehicles to use for this problem. If no one in the group owns a vehicle, pick a vehicle you would like to “use to drive to school”.

1) List all variables and their values.

2) Describe the mathematical model developed to find a solution.

3) What assumptions can you make about your model?

4) Which option did you determine is more economical? Why?

5) How do you know you have a good model?

6) Pick two different vehicles: one that gets more miles per gallon than your vehicle and one that gets less. Which option is more economical with these vehicles? Why? Show all work.

7) What do the results from above tell you about the sensitivity of your model?

8) What other considerations would contribute to your decision about which gas station to use? (Give your reasoning – whether it would be worthwhile or not to drive to the gas station that is priced lower than the others?)

REFLECTION

1) Explain the process your team used to develop a solution.

2) Explain the mathematics used to develop your team’s solution.

3) How did each of your teammates participate in the modeling process?

4) What did you learn from the other members of your team?

5) Did you revise your model at any point during the activity? If so, why? How did you fix the model?

6) Can you identify a math idea that was key to your ability to develop a model?

7) What advice would you give to a classmate (or yourself) prior to developing a mathematical model?

8) What was the most unexpected aspect of this project?