Hi, Thank you very much for your response. In fact, it is not framed by me. It is a project given to one of my students. I am working on this. I use certain variables and parameters. I thought others could come out with different variables and parameters other than those I am using. I once again post the question under discussion in detail. It would be great if you can share your ideas, views or guidance.
FILLING UP THE PETROL TANK
To the student: The work that you produce to address the questions in this task should be a report
that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question
and answer" format.
In this task, you will develop a mathematical model that helps motorists decide which of
the following two options is more economical.
Option 1: to buy petrol from a station on their normal route at a relatively higher price.
Option 2: to drive an extra distance out of their normal route to buy cheaper petrol.
Consider a situation in which two motorists, Arwa and Bao, share the same driving route but own
different sized vehicles. Arwa fills up her vehicle's tank at a station along her normal route for
US$ p1 per litre. On the other hand, Bao drives an extra d kilometres out of his normal route to fill up his vehicle's tank for US$ p2 per litre where p2 < p1 .
Choose suitable parameters for Arwa's and Bao's vehicles. Justify your choices.
Suppose p1 is US$1.00 , p2 is US$0.98 and d is10 km. Which motorist
is getting the better deal? Show all calculations and justify any assumptions you make.
_ On a spreadsheet, choose several sets of values for p1 , p2 and d to investigate further.
_ Define a set of variables that would be relevant in the above situation.
“Effective litres" is a method of comparing the cost of petrol bought under the two options
described above. Effective litres, for a given vehicle, are those litres used when the vehicle travels its normal route.
_ Use your variables and parameters to write algebraic expressions for E1 and E2 which
represent the cost per effective litre under options 1 and 2 respectively.
_ Write a model that helps motorists decide on the more economical option for their
In the remainder of this task, you need to consider the two vehicles you have chosen for Arwa and Bao.
_ Use your model to find the farthest distance that Bao should drive to obtain a 2 % price
_ Investigate the relationship between d and p2 when E2 is kept constant (e.g. US$0.90,
US$1.00, … etc.). Use technology to draw a family of curves for Arwa's vehicle. Repeat
for Bao's vehicle.
_ For E2 _ US$0.90 , provide Arwa with information on three different stations that yield
this same cost per effective litre. Discuss how such information may be useful to Arwa.
_ For E2 _ US$1.00 and p2 _ US$0.80 , compare the maximum distance that each motorist
should drive and still save money.
Arwa is a busy person and wonders whether the saving in money would be worth the time she
would lose in extra driving.
_ Modify your model to account for the time taken to drive to and from an off-route station.
Clearly justify any assumptions you make.