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1. 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.

(4)

(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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Updated: November 8, 2017
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