Moderate -0.5 This is a standard dynamic programming problem from Decision Maths D2 requiring systematic application of the tabular method to find optimal ordering. While it involves multiple steps, the technique is algorithmic and well-practiced, making it easier than average A-level questions which typically require more mathematical insight or problem-solving.
5 Robert is planning to renovate four houses, \(A , B , C\) and \(D\), at the rate of one per month. The houses can be renovated in any order but the costs will vary because some of the materials left over from renovating one house can be used for the next one. The expected profits, in hundreds of pounds, are given in the table below.
Insert table from below. May: 8 of their calculations/profits correct
B1, M1, A1, B1
Exactly 12 rows seen at this stage; All profits correct; Their 6 maxima values identified (PI by further work)
April: 9 or more calculations/profits correct
B1, M1, A1
Exactly 12 rows seen at this stage; All profits correct
March: 3 or more calculations/profits correct
M1, A1
All profits correct
Order DBCA
B1
£28100
B1
Must include '£'; Allow equivalent in words
| Answer | Marks | Guidance |
|--------|-------|----------|
| Insert table from below. May: 8 of their calculations/profits correct | B1, M1, A1, B1 | Exactly 12 rows seen at this stage; All profits correct; Their 6 maxima values identified (PI by further work) |
| April: 9 or more calculations/profits correct | B1, M1, A1 | Exactly 12 rows seen at this stage; All profits correct |
| March: 3 or more calculations/profits correct | M1, A1 | All profits correct |
| Order DBCA | B1 | |
| £28100 | B1 | Must include '£'; Allow equivalent in words |
5 Robert is planning to renovate four houses, $A , B , C$ and $D$, at the rate of one per month. The houses can be renovated in any order but the costs will vary because some of the materials left over from renovating one house can be used for the next one. The expected profits, in hundreds of pounds, are given in the table below.
\hfill \mbox{\textit{AQA D2 2016 Q5 [11]}}