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A contractor intends to transport 1,000 bags of cement using a lorry and a pick up. The lorry can carry a maximum of 80 bags while a pick up can carry a maximum of 20 bags. The pickup has to make more than twice the number of trips the lorry makes and the total number of trips has to be less than 30. The cost per trip is sh. 2,000 for the lorry and sh 900 for the pickup and the contractor wishes to minimize cost. Let x and y be the trips for the lorry and pickup respectively.

  1. State the objective function.
  2. Write down all the inequalities which govern the condition above.

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  1. 2000x + 900y 
  2. y > 2x   
    x + y <30   
    80x + 20y ≥ 1000, 4x + y ≥ 50

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