| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Formulation from word problem |
| Difficulty | Moderate -0.8 This is a standard textbook linear programming problem with straightforward constraints and objective function. The formulation requires careful reading but uses routine techniques (defining variables, writing inequalities, graphical solution). The multi-part structure guides students through the method step-by-step, and LP problems at D1 level are typically more mechanical than conceptually challenging. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables |
| Answer | Marks | Guidance |
|---|---|---|
| A | B | C |
| A | – | 7 |
| B | 7 | – |
| C | – | 5 |
| D | – | 3 |
| E | 12 | 6 |
| F | – | 6 |
Question 5:
5
5 Leone is designing her new garden. She wants to have at least 1000m2, split between lawn and
flower beds.
Initial costs are £0.80 per m2 for lawn and £0.40 per m2 for flowerbeds. Leone’s budget is £500.
Leone prefers flower beds to lawn, and she wants the area for flower beds to be at least twice the
area for lawn. However, she wants to have at least 200m2 of lawn.
Maintenance costs each year are £0.15 per m2 for lawn and £0.25 per m2 for flower beds. Leone
wants to minimize the maintenance costs of her garden.
(i) Formulate Leone’s problem as a linear programming problem. [7]
(ii) Produce a graph to illustrate the inequalities. [6]
(iii) Solve Leone’s problem. [2]
(iv) If Leone had more than £500 available initially, how much extra could she spend to minimize
maintenance costs? [1]
6 In a factory a network of pipes connects 6 vats, A, B, C, D, E and F. Two separate connectors need
to be chosen from the network The table shows the lengths of pipes (metres) connecting the 6 vats.
A B C D E F
A – 7 – – 12 –
B 7 – 5 3 6 6
C – 5 – 8 4 7
D – 3 8 – 1 5
E 12 6 4 1 – 7
F – 6 7 5 7 –
(i) Use Kruskal’s algorithm to find a minimum connector. Show the order in which you select
pipes, draw your connector and give its total length. [5]
(ii) Produce a new table excluding the pipes which you selected in part (i). Use the tabular form
of Prim’s algorithm to find a second minimum connector from this reduced set of pipes. Show
your working, draw your connector and give its total length. [7]
(iii) The factory manager prefers the following pair of connectors:
{AB, BC, BD, BE, BF} and {AE, BF, CE, DE, DF}.
Give two possible reasons for this preference. [4]
A | B | C | D | E | F
A | – | 7 | – | – | 12 | –
B | 7 | – | 5 | 3 | 6 | 6
C | – | 5 | – | 8 | 4 | 7
D | – | 3 | 8 | – | 1 | 5
E | 12 | 6 | 4 | 1 | – | 7
F | – | 6 | 7 | 5 | 7 | –Leone is designing her new garden. She wants to have at least 1000 m$^2$, split between lawn and flower beds.
Initial costs are £0.80 per m$^2$ for lawn and £0.40 per m$^2$ for flowerbeds. Leone's budget is £500.
Leone prefers flower beds to lawn, and she wants the area for flower beds to be at least twice the area for lawn. However, she wants to have at least 200 m$^2$ of lawn.
Maintenance costs each year are £0.15 per m$^2$ for lawn and £0.25 per m$^2$ for flower beds. Leone wants to minimize the maintenance costs of her garden.
\begin{enumerate}[label=(\roman*)]
\item Formulate Leone's problem as a linear programming problem. [7]
\item Produce a graph to illustrate the inequalities. [6]
\item Solve Leone's problem. [2]
\item If Leone had more than £500 available initially, how much extra could she spend to minimize maintenance costs? [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI D1 2007 Q5 [16]}}