A2 October 2021 Q3
3. The table below shows the cost, in pounds, of transporting one unit of stock from each of four supply points, A, B, C and D, to four sales points, P, Q, R and S. It also shows the number of units held at each supply point and the number of units required at each sales point.
A minimum cost solution is required.
| P | Q | R | S | Supply | |
|---|---|---|---|---|---|
| A | 18 | 19 | 17 | 13 | 28 |
| B | 16 | 15 | 14 | 19 | 43 |
| C | 21 | 17 | 22 | 23 | 29 |
| D | 16 | 20 | 19 | 21 | 36 |
| Demand | 25 | 41 | 40 | 30 |
- shadow costs
- improvement indices
- entering cell and exiting cell
| Scheme | Marks | AO | |||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B1 | 1.1b | |||||||||||||||||||||||||
| (1) |
Notes
B1: cao
| Scheme | Marks | AO | ||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| M1 A1 | 2.1 1.1b | ||||||||||||||||||||||||||||||||||||||||||||||||||
| (2) |
Notes
M1: A valid route shown, only one empty square used, \(\theta\)’s balance
A1: cao
| Scheme | Marks | AO | ||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| M1 A1 | 1.1b 1.1b | ||||||||||||||||||||||||||||||||||||||||||||||||||
| M1 | 1.1b | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Entering cell is DP and exiting cell is AP | A1 | 2.2a | ||||||||||||||||||||||||||||||||||||||||||||||||||
| (4) |
Notes
M1: Finding all 8 shadow costs and the 9 improvement indices for the correct 9 entries
A1: Shadow costs and II cao
M1: A valid route shown, their most negative II chosen, only one empty square used, \(\theta\)’s balance
A1: cao – including the deduction (and stating) of all entering and exiting cells
| Scheme | Marks | AO |
|---|---|---|
| (£)2258 | B1 | 1.1b |
| (1) |
Notes
B1: cao
| Scheme | Marks | AO | ||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| M1 A1 | 2.1 1.1b | ||||||||||||||||||||||||||||||||||||
| A negative II so solution is not optimal | A1 | 2.4 | ||||||||||||||||||||||||||||||||||||
| (3) | ||||||||||||||||||||||||||||||||||||||
| (11 marks) |
Notes
M1: Finding all 8 shadow costs and all 9 negative improvement indices or sufficient number of shadow costs for at least 1 negative II found – this mark is dependent on the previous M mark in (b) which will therefore indicate a correct mathematical argument leading from the initial solution to the confirmation or not of the optimality of the current solution
A1: cao negative II from correct working
A1: cso including the correct reasoning that the solution is not optimal because there is a negative II