7. A clothing manufacturer can export a maximum of five batches of shirts each year. Each exported batch contains just one type of shirt, the types being T-shirts, Rugby shirts and Polo shirts. The table below shows the profit, in £ 1000 s, for the number of each exported batch type. 2.

1. 	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   	1	2	3	4	Supply
   A					33
   B					21
   C					25
   Demand	21	17	28	13

   3.

   	B plays 1	B plays 2	B plays 3
   A plays 1	0	- 2	6
   A plays 2	3	4	1
   A plays 3	- 1	1	- 3

   4.

   	1	2	3	4
   A	53	84	-	20
   B	87	72	41	38
   C	70	51	52	25
   D	45	-	81	70

   5. (a)
2. You may not need to use all of these tableaux

   b.v.	\(x\)	\(y\)	\(z\)	\(r\)	\(s\)	\(t\)	Value
   \(r\)	15	- 2	3	1	0	0	180
   \(s\)	10	1	1	0	1	0	80
   \(t\)	1	6	- 2	0	0	1	100
   \(P\)	- 1	- 2	- 5	0	0	0	0

   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
   \(P\)

   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
   \(P\)

   b.v.	\(x\)	\(y\)	\(z\)	\(r\)	\(s\)	\(t\)	Value	Row Ops
   \(P\)

3. 
   6. (a) Value of initial flow
4. Capacity of cut \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{d5798c81-290a-4e4b-aa46-497b62ca899b-20_1931_1099_507_408} \captionsetup{labelformat=empty} \caption{Diagram 1}
   \end{figure} \includegraphics[max width=\textwidth, alt={}, center]{d5798c81-290a-4e4b-aa46-497b62ca899b-21_1874_953_653_589}
   7. You may not need to use all the rows of this table

   Stage	State	Action	Dest.	Value
   T-shirt

   Stage	State	Action	Dest.	Value

   Maximum annual profit £ \(\_\_\_\_\)