Data provided
For each location: V = (424) + D/14.8; T = V*P; F = 42  D/14.8; M = (2D*60)/60 = 2D 
Apply the above formulae for each petrol station, using route finder to estimate distances.
Check assumption that all stations are within the range of Sam’s car which has 4L of petrol: 56 km
For 7 Eleven (Albany Creek): D = 16.7, P = 120.7 so, V = 38 + 16.7/14.08 = 39.19 (L) T= 39.13*120.7 = 4730.233 = 47.30 ($) F = 42 – 16.7/14.08 = 40.81 (L) M = 2*16.7 = 33.4 (min) Similar calculations for all petrol stations give: 
With 4 litres (56 km) of petrol in the tank all fuel outlets are well within Sam’s margin of safety. The cheapest fuel option is also the furthest away and will result in the least fuel in the tank when the car returns. All other choices see the car returned with less than a litre short of a full tank, while using the closest station will result in the most expensive fuel charge. Deciding the ‘best’ station to use involves considering the mathematical calculations together with aspects of the real decisionmaking context.
It was assumed that travel time was not a main issue in terms of calculating costs. However, it might serve as a tie breaker in deciding between two closely similar options. Here Puma at Everton Park is cheaper in terms of fuel costs than the closest option (Noonan's). It is also convenient regarding travel time and returns the car with a nearly full tank. Apart from the additional travel time, the extra distance (13.4 km), to and from the cheapest option (7Eleven) would erode most of the cost saving in using that location. Decision — choose Puma. 
The model has provided a basis for necessary decision making by Sam. The recommendation is based on a combination of (checked) mathematical calculations and realworld considerations relevant to the context. Data values used in the calculations have been checked.
Additionally, assumptions have been reviewed and their place in model formulation, solution, and interpretation verified. No obvious omissions were identified given the level of accuracy involved. In summary, the modelling has enabled a solution to be recommended for the original realworld problem. 
If the modelling process has been documented as in the preceding sections, the essence of the report already exists. It can be constructed formally by integrating content from sections 1 to 6, under the respective headings. Additional material can be introduced for purposes of elaboration, completeness, or overall coherence.

The assumptions remain the same — except that Sam is replaced by a driver of any car and the journey for fuel starts and finishes at the home address. To apply to any car, we create variables as required from the specific data items given in the original problem for a specific car.
Quantities needed for decision making
Then: Provided D < L*c (ensures car can reach location without running out of fuel) V = (C – L) + D/c T = V*P = [(C – L) + D/c]P F = C – D/c M = 2D For Sam we have: Provided that D < 56.3 (km) V = 38 + 0.071D (litres) T = (38 + 0.071D) P (dollars) F = 42 – 0.071D (litres) M = 2D (minutes) Unit checks In addition to checking calculations step by step, an additional separate check is to see that all mathematical expressions are correct in terms of units. For example in the formula T = [(C – L) + D/c]P , ‘T’ is measured in cents, so the two terms on the right hand side must also be measured in cents. (CL) P has units of (litres) x (cents/litre) and the litres cancel to leave us with ‘cents’ as required. (D/c) P has units of (km)/(km/litre) x (cents/litre). The litres and km cancel – leaving cents. We know our formula is correct, at least as far as units are concerned. With formulae or equations with many variables, it is easy to leave one out, or perhaps write an x2 as x. A units check will discover this, and enable the error to be corrected, although it will not pick up mistakes in arithmetic. 
Check using values provided for Sam’s car refuelling at Albany Creek: C = 42; L = 4; c = 14.08; D = 16.7; P = 120.7 gives T = 47.30; F = 40.81; M = 33 as before. Now individual values can be entered in formulae to provide decision data for any vehicle and location. Given a set of petrol stations seen as relevant a spreadsheet can be designed, to provide decision making data as petrol prices change. Here is an extract. A list of potential petrol stations is entered in column A. (For purposes of illustration the stations A – D are those given in the problem, but any number can be entered.) Columns B and C contain the distance and price data for these stations. Column D contains parameters relevant to the specific situation and can be adapted to any circumstances or vehicle. The Cell formulae in Row 2 define the numerical values for petrol station A as follows (also converting prices to dollars and times to minutes). FORMULA IN E2: = (($D$7– $D$3) +B2/$D$5) FORMULA IN F2: = (E2*C2) FORMULA IN G2: = ($D$7  B2/$D$5) FORMULA IN H2: =(2*B2/$D$9*60) Select contents of E2, F2, G2, H2 and copy down as a block as far as row 5, to generate the corresponding values for other Petrol stations as shown. A spreadsheet will provide decision making criteria instantaneously when new data are entered. 
In addition to providing a solution to the original problem, which validates its content, the approach provides a method applicable to any vehicle requiring fuel at any location, This can be verified for any aspect of the solution – evidence for which is provided in the detail of the documentation and can be referred to as such.
The spreadsheet gives instantaneous advice for new situations by instantaneously processing corresponding data. When prices change by amounts exceeding 40 cents/litre, and neighbouring fuel outlets differ by hours in implementing the change, savings available are rendered more obvious when such comparisons are available. 
Modelling

Enablers

Members 