| Exam Board | OCR |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Integer solution optimization |
| Difficulty | Moderate -0.3 This is a standard D1 linear programming question requiring reading inequalities from a graph, finding vertices by solving simultaneous equations, evaluating an objective function, and finding an integer solution. While multi-part, each step uses routine techniques with no novel insight required. The integer optimization in part (iv) is straightforward—test nearby integer points. Slightly easier than average due to the mechanical nature of the tasks. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables |
Question 3:
B1 Correct answer3 The constraints of a linear programming problem are represented by the graph below. The feasible region is the unshaded region, including its boundaries.\\
\includegraphics[max width=\textwidth, alt={}, center]{ccb12789-cd5f-40dc-9f10-f8bb45399580-4_919_917_322_575}\\
(i) Obtain the four inequalities that define the feasible region.\\
(ii) Calculate the coordinates of the vertices of the feasible region, giving your values as fractions.
The objective is to maximise $P = x + 4 y$.\\
(iii) Calculate the value of $P$ at each vertex of the feasible region. Hence write down the coordinates of the optimal point, and the corresponding value of $P$.
Suppose that the solution must have integer values for both $x$ and $y$.\\
(iv) Find the coordinates of the optimal point with integer-valued $x$ and $y$, and the corresponding value of $P$. Explain how you know that this is the optimal solution.
\hfill \mbox{\textit{OCR D1 2012 Q3 [13]}}