Easy -1.2 This is a straightforward D1 linear programming question requiring students to shade a feasible region defined by linear inequalities. It involves routine skills of plotting lines and identifying the correct region, which is a standard textbook exercise with no problem-solving complexity beyond mechanical application of the graphical method.
Float on F is twice float on D: \(\Rightarrow 22 - 8 - y = 2(8 - 3 - x)\) (oe)
B1
cao (any equivalent form) – allow \(14 - y = 2(5-x)\) or \(14 - y = 10 - 2x\)
BFDM is 10 less than critical path: \(\Rightarrow 3 + x + y + 3 = 26 - 10\) (oe)
B1
cao (any equivalent form) – allow \(x + y + 6 = 16\)
\(x + y = 10\) and \(-2x + y = 4\) solved simultaneously
M1
Setting up two equations both including \(x\) and \(y\), attempt to solve for both
\(x = 2,\ y = 8\)
A1
cao – if both correct values stated without working send to review
Question 4(b):
Answer
Marks
Guidance
Answer
Marks
Guidance
Gantt chart with at least nine activities labelled including at least five floats (scheduling diagram scores M0)
M1
Critical activities dealt with correctly appearing just once (A, G, I, L) and three non-critical activities dealt with correctly
A1
Any six non-critical activities correct
A1
Not dependent on previous A mark
Completely correct Gantt chart (exactly thirteen activities appearing just once)
A1
Question 4(c):
Answer
Marks
Guidance
Answer
Marks
Guidance
Lower bound is 4 workers e.g. activities F, I, J and K together with \(15 < \text{time} < 16\)
M1 A1
Must state correct number of workers (4) and correct activities (F, I, J, K) with any numerical time stated or correct number of workers with time in interval \(15 \leqslant t \leqslant 16\); completely correct statement with additional incorrect statement scores A0
# Question 4(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Float on F is twice float on D: $\Rightarrow 22 - 8 - y = 2(8 - 3 - x)$ (oe) | B1 | cao (any equivalent form) – allow $14 - y = 2(5-x)$ or $14 - y = 10 - 2x$ |
| BFDM is 10 less than critical path: $\Rightarrow 3 + x + y + 3 = 26 - 10$ (oe) | B1 | cao (any equivalent form) – allow $x + y + 6 = 16$ |
| $x + y = 10$ and $-2x + y = 4$ solved simultaneously | M1 | Setting up two equations both including $x$ and $y$, attempt to solve for both |
| $x = 2,\ y = 8$ | A1 | cao – if both correct values stated without working send to review |
# Question 4(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gantt chart with at least nine activities labelled including at least five floats (scheduling diagram scores M0) | M1 | |
| Critical activities dealt with correctly appearing just once (A, G, I, L) and three non-critical activities dealt with correctly | A1 | |
| Any six non-critical activities correct | A1 | Not dependent on previous A mark |
| Completely correct Gantt chart (exactly thirteen activities appearing just once) | A1 | |
# Question 4(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower bound is 4 workers e.g. activities F, I, J and K together with $15 < \text{time} < 16$ | M1 A1 | Must state correct number of workers (4) and correct activities (F, I, J, K) with any numerical time stated **or** correct number of workers with time in interval $15 \leqslant t \leqslant 16$; completely correct statement with additional incorrect statement scores A0 |
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