| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Transportation problem: stepping-stone method |
| Difficulty | Standard +0.3 This is a standard algorithmic question testing the north-west corner method and stepping-stone method for transportation problems. While it involves multiple steps and careful bookkeeping, it requires only mechanical application of well-defined algorithms taught in D2 with no problem-solving insight or novel reasoning. The procedures are routine for this module, making it slightly easier than average A-level difficulty overall. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06c Working with constraints: algebra and ad hoc methods7.06d Graphical solution: feasible region, two variables |
| P | Q | R | S | Supply | |
| A | 28 | 32 | 33 | 27 | 13 |
| B | 31 | 29 | 26 | 31 | 4 |
| C | 30 | 26 | 29 | 32 | 12 |
| D | 25 | 30 | 28 | 34 | 11 |
| Demand | 11 | 10 | 11 | 8 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(B1\) | (1) |
| (b) | \(M1 A1\) | (4) |
| (c) | \(M1 A1\) | — |
| \(A1ft\) | — | Valid route, only one empty square used, 0's balance |
| \(A1\) | (4) | Correct route; Entering square AS, exiting square AQ (0 = 2) |
| (d) | \(B1\) | (1) |
| 10 marks |
**(a)** | $B1$ | (1) | Completing the table correctly |
**(b)** | $M1 A1$ | (4) | Finding 8 shadow costs; Shadow costs CAO |
**(c)** | $M1 A1$ | — | Shadow costs CAO |
| $A1ft$ | — | Valid route, only one empty square used, 0's balance |
| $A1$ | (4) | Correct route; Entering square AS, exiting square AQ (0 = 2) |
**(d)** | $B1$ | (1) | CAO |
| | 10 marks | |
---\begin{enumerate}
\item Four bakeries, $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D , supply bread to four supermarkets, $\mathrm { P } , \mathrm { Q } , \mathrm { R }$ and S . The table gives the cost, in pounds, of transporting one lorry load of bread from each bakery to each supermarket. It also shows the number of lorry loads of bread at each bakery and the number of lorry loads of bread required at each supermarket. The total cost of transportation is to be minimised.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
& P & Q & R & S & Supply \\
\hline
A & 28 & 32 & 33 & 27 & 13 \\
\hline
B & 31 & 29 & 26 & 31 & 4 \\
\hline
C & 30 & 26 & 29 & 32 & 12 \\
\hline
D & 25 & 30 & 28 & 34 & 11 \\
\hline
Demand & 11 & 10 & 11 & 8 & \\
\hline
\end{tabular}
\end{center}
(a) Use the north-west corner method to obtain a possible solution.
A partly completed table of improvement indices is given in Table 1 in the answer book.\\
(b) Complete Table 1.\\
(c) Taking the most negative improvement index to indicate the entering cell, use the steppingstone method once to obtain an improved solution. You must make your route clear and state your entering cell and exiting cell.\\
(d) State the cost of your improved solution.\\
\hfill \mbox{\textit{Edexcel D2 2014 Q1 [10]}}