Standard +0.3 This is a standard Hungarian algorithm application with simple restrictions (indicated by asterisks). The algorithm itself is mechanical and well-practiced in D2, requiring only systematic row/column reduction and assignment. The restrictions add minimal complexity as they're clearly marked and handled by treating those cells as unavailable.
2 Alan, Beth, Callum, Diane and Ethan work for a restaurant chain. The costs, in pounds, for the five people to travel to each of five different restaurants are recorded in the table below.
Alan cannot travel to restaurant 1 and Beth cannot travel to restaurants 3 and 5, as indicated by the asterisks in the table.
Using column or row minima. The 'x' could be a number \(\ge 20\), or a 'dash', or omitted. At least 4 rows or columns correct (lines, or lack of, are not needed here)
M1
Using row or column minima. At least 4 columns or rows correct
m1
All numbers correct
A1
Correct use of 4 lines
B1
Reduce all uncovered elements by 1, Leave all one line elements, Add 1 to all double line elements. Condone 1 (new) slip, but must have score M1m1
m1
All numbers correct
A1
Correct use of 5 lines AND optimal. A4, B2, C5, D3, E1 or A4, B1, C5, D2, E3 or A5, B2, C4, D3, E1 or A5, B1, C4, D2, E3
B1, B1
Three correct allocations; All 4 correct and no extras
\([E]\) 61
B1
Condone omission of units
| Answer | Marks | Guidance |
|--------|-------|----------|
| Using column or row minima. The 'x' could be a number $\ge 20$, or a 'dash', or omitted. At least 4 rows or columns correct (lines, or lack of, are not needed here) | M1 | |
| Using row or column minima. At least 4 columns or rows correct | m1 | |
| All numbers correct | A1 | |
| Correct use of 4 lines | B1 | |
| Reduce all uncovered elements by 1, Leave all one line elements, Add 1 to all double line elements. Condone 1 (new) slip, but must have score **M1m1** | m1 | |
| All numbers correct | A1 | |
| Correct use of 5 lines AND optimal. A4, B2, C5, D3, E1 or A4, B1, C5, D2, E3 or A5, B2, C4, D3, E1 or A5, B1, C4, D2, E3 | B1, B1 | Three correct allocations; All 4 correct and no extras |
| $[E]$ 61 | B1 | Condone omission of units |
2 Alan, Beth, Callum, Diane and Ethan work for a restaurant chain. The costs, in pounds, for the five people to travel to each of five different restaurants are recorded in the table below.
Alan cannot travel to restaurant 1 and Beth cannot travel to restaurants 3 and 5, as indicated by the asterisks in the table.
\hfill \mbox{\textit{AQA D2 2016 Q2 [10]}}