# Question 5

## (a)
| $a$ | $b$ | $c$ | $d$ | $e$ | $f$ | $f = 0$? |
|---|---|---|---|---|---|---|
| 645 | 255 | 2.53 | 2 | 510 | 135 | No |
| 255 | 135 | 1.89 | 1 | 135 | 120 | No |
| 135 | 120 | 1.13 | 1 | 120 | 15 | No |
| 120 | 15 | 8 | 8 | 120 | 0 | Yes |

Finds the H.C.F of $a$ and $b$ | M1 A1

## (b)
The answer is 15 | A1

The first row would be
| $a$ | $b$ | $c$ | $d$ | $e$ | $f$ | $f = 0$? |
|---|---|---|---|---|---|---|
| 255 | 645 | 0.40 | 0 | 0 | 255 | No |

But the second row would then be the same as the first row above, and the solution thereafter would be the same. | M1 A1

## (c)
| A | E | D | I | L | P |
| C | G | H | M |
| B | F | J | K | N |

| A1 A1 A1 (7)

(11 marks total)

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# Question 8

## (a)
$x + y \geq 380$ | B1
$y \geq 125$ | B1
$2x + 4y \leq 1200$ | B1

(3 marks)

## (b)
$c = 3x + 2y$ | B1

(1 mark)

## (c)
Graph showing feasible region with lines:
- $x + y = 380$
- $y = 125$
- $2x + 4y = 1200$

| B1 B1 B1 B1 (4)

## (d)
Use of profit line or points testing | M1

Minimum at intersection of $x + y = 380$ and $2x + 4y = 1200$

$x = 160$, $y = 120$, cost $= £920$ | A1 A1 (3)

Maximum at intersection of $y = 125$ and $2x + 4y = 1200$

$x = 350$, $y = 125$, cost $= £1300$ | M1 A1 A1 (3)

(14 marks total)