# Question 2:

## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Subtract each entry from a constant (eg 10) | B1 | Valid method to convert minimisation to maximisation |

## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $10 -$ each entry giving correct matrix | B1 | Subtracting each entry from a constant (may use other constant, but require matrix with no negative values before reducing) |
| Reduce rows (resulting in a correct matrix with a 0 in each row) | M1 | Correct method for reducing rows (may be implied from correct matrix) |
| Reduce columns resulting in reduced cost matrix as given | A1 | Correct method for reducing columns, resulting in reduced cost matrix as given. Need evidence of method, not just the correct (given) matrix |

## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cross through zeros using four lines; first augmentation correct | M1, A1 | First augmentation started, having crossed through all 0's using at least 4 lines (may be implied from correct augmented matrix) |
| Second augmentation, crossing through 0's using exactly five lines | M1 | May be implied from augmented matrix |
| Correct matrix after second augmentation | A1 | cao |
| Fred cooks on Tuesday | B1 | Follow through their final matrix (do not need to give allocation) |

## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $B=$ Thurs; $C=$ Mon; $D=$ Fri; $E=$ Weds | M1 | A valid matching for B, C, D and E from their final matrix (ignoring what candidate says about Alice and Fred) |
| $A=$ Sun; $F=$ Tues | A1 | This matching (cao), including A and F |

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