A football team is performing badly. The manager of the team can buy some new players to try and gain some extra points.
A very simple model of the manager’s situation is as follows.
He can buy new attackers for £3 million each and new defenders for £1 million each.
Each attacker will help the club to get two more points and each defender will help the club to get one more point.
The manager has £12 million to spend.
The team must gain at least 5 more points.
The manager must buy at least one defender and at least one attacker.
He must spend at least £6 million.
The manager buys x attackers and y defenders.
(a) Express the manager’s situation in terms of inequalities suitable for investigating the problem by linear programming.
(b) On the graph below, draw a suitable diagram to enable the problem to be investigated graphically, indicating the feasible region.
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