7. A company has purchased a plot of land and has decided to build four holiday homes, A, B, C and D, on the land at the rate of one home per year.
The company expects that the construction costs each year will vary, depending on which houses have already been constructed and which house is currently under construction. The expected construction costs, in thousands of pounds, are shown in the table below.
| \cline { 2 - 7 }
\multicolumn{1}{c|}{} | A | B | C | D | E | F |
| A | - | 53 | 47 | 39 | 35 | 40 |
| B | 53 | - | 32 | 46 | 41 | 43 |
| C | 47 | 32 | - | 51 | 47 | 37 |
| D | 39 | 46 | 51 | - | 36 | 49 |
| E | 35 | 41 | 47 | 36 | - | 42 |
| F | 40 | 43 | 37 | 49 | 42 | - |
\begin{table}[h]
| 1 | 2 | 3 | 4 | Supply |
| A | 17 | 20 | 23 | 14 | 25 |
| B | 16 | 15 | 19 | 22 | 29 |
| C | 19 | 14 | 11 | 15 | 32 |
| Demand | 28 | 17 | 23 | 18 | |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
2.
You may not need to use all of these tables
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Table 1}
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
\end{table}
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
| 1 | 2 | 3 | 4 | Supply |
| A | | | | | 25 |
| B | | | | | 29 |
| C | | | | | 32 |
| Demand | 28 | 17 | 23 | 18 | |
3.
| A | B | C | D | E |
| Frank | 5 | 0 | 7 | 3 | 4 |
| Gill | 5 | 3 | 8 | 10 | 1 |
| Harry | 4 | 3 | 7 | 9 | 0 |
| Imogen | 6 | 3 | 6 | 5 | 4 |
| Jiao | 0 | 2 | 7 | 3 | 2 |
You may not need to use all of these tables
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| \(F\) | | | | | |
| \(G\) | | | | | |
| \(H\) | | | | | |
| \(I\) | | | | | |
| \(J\) | | | | | |
| Stephen plays 1 | Stephen plays 2 | Stephen plays 3 |
| Eugene plays 1 | 4 | 5 | 0 |
| Eugene plays 2 | -2 | 1 | 1 |
| Eugene plays 3 | -3 | -4 | 3 |
4.
5. (a)
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value |
| | | | | | | 30 |
| | | | | | | 60 |
| | | | | | | 80 |
| | | | | | | 0 |
You may not need to use all of these tableaux
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value | Row Ops |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| \(P\) | | | | | | | | |
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value | Row Ops |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| \(P\) | | | | | | | | |
| b.v. | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value | Row Ops |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| \(P\) | | | | | | | | |
6. (a) Value of initial flow
(b) and (c)
\includegraphics[max width=\textwidth, alt={}, center]{e0c66144-9e34-42fc-9f40-a87a49331483-20_725_1251_404_349}
\section*{Diagram 1}
\includegraphics[max width=\textwidth, alt={}]{e0c66144-9e34-42fc-9f40-a87a49331483-20_1070_1264_1322_349}
\section*{Diagram 2}
(d)
(e)
\includegraphics[max width=\textwidth, alt={}, center]{e0c66144-9e34-42fc-9f40-a87a49331483-21_714_1385_1306_283}
\section*{Diagram 3}
(f)
7. (a)
| Stage | State | Action | Dest. | Value |
| 1 | ABC | D | ABCD | 65* |
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\includegraphics[max width=\textwidth, alt={}]{e0c66144-9e34-42fc-9f40-a87a49331483-24_2642_1833_118_118}