| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Transportation problem formulation |
| Difficulty | Moderate -0.8 This is a standard transportation problem formulation requiring only systematic translation of given information into LP format. No problem-solving or optimization is required—just defining variables, writing the objective function from the profit table, and stating supply/demand constraints. This is routine textbook material for D2, easier than average A-level questions which typically require some problem-solving. |
| Spec | 7.06a LP formulation: variables, constraints, objective function |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | \(B _ { 1 }\) | \(B _ { 2 }\) | \(B _ { 3 }\) |
| \(F _ { 1 }\) | 20 | 14 | 17 |
| \(F _ { 2 }\) | 18 | 19 | 19 |
| \(F _ { 3 }\) | 15 | 17 | 23 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | H | HK |
| I | IK | |
| J | JK |
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\item A glazing company runs a promotion for a special type of window. As a result of this the company receives orders for 30 of these windows from business $B _ { 1 } , 18$ from business $B _ { 2 }$ and 22 from business $B _ { 3 }$. The company has stocks of 20 of these windows at factory $F _ { 1 } , 35$ at factory $F _ { 2 }$ and 15 at factory $F _ { 3 }$. The table below shows the profit, in pounds, that the company will make for each window it sells according to which factory supplies each business.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & $B _ { 1 }$ & $B _ { 2 }$ & $B _ { 3 }$ \\
\hline
$F _ { 1 }$ & 20 & 14 & 17 \\
\hline
$F _ { 2 }$ & 18 & 19 & 19 \\
\hline
$F _ { 3 }$ & 15 & 17 & 23 \\
\hline
\end{tabular}
\end{center}
The glazing company wishes to supply the windows so that the total profit is a maximum.\\
Formulate this information as a linear programming problem.\\
\begin{enumerate}[label=(\alph*)]
\item State your decision variables.
\item Write down the objective function in terms of your decision variables.
\item Write down the constraints and state what each one represents.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q1 [6]}}