| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Transportation problem formulation |
| Difficulty | Moderate -0.5 This is a standard transportation problem formulation requiring students to define decision variables (x_ij for amounts transported), write the objective function (minimize total cost), and state supply/demand constraints. It's mechanical application of a taught method with no problem-solving insight needed, making it easier than average, though the bookkeeping of 9 variables and multiple constraints requires care. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations |
| S | T | U | |
| F | 23 | 31 | 46 |
| G | 35 | 38 | 51 |
| H | 41 | 50 | 63 |
3. Three depots, F, G and H, supply petrol to three service stations, S, T and U. The table gives the cost, in pounds, of transporting 1000 litres of petrol from each depot to each service station.
F, G and H have stocks of 540000,789000 and 673000 litres respectively.\\
S, T and U require 257000,348000 and 412000 litres respectively. The total cost of transporting the petrol is to be minimised.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& S & T & U \\
\hline
F & 23 & 31 & 46 \\
\hline
G & 35 & 38 & 51 \\
\hline
H & 41 & 50 & 63 \\
\hline
\end{tabular}
\end{center}
Formulate this problem as a linear programming problem. Make clear your decision variables, objective function and constraints.\\
\hfill \mbox{\textit{Edexcel D2 2006 Q3 [8]}}