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7 marksLinear Programming

CAPE Applied Mathematics Unit 2 · 2015 · Paper 2 · Question 1(a)(i)b)

A firm manufactures glass and plastic bottles, each passing through a sterilizing machine and a capping machine. A case of glass bottles takes 4 minutes to sterilize and 3 minutes to cap. A case of plastic bottles takes 4 minutes to sterilize and 6 minutes to cap. Each machine is available for 50 hours per week. Profits are 20 per case of glass bottles and 15 per case of plastic bottles.

Formulate the inequalities to be used to solve this problem.

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Other parts of this question

  1. 1(a)(i)a)By identifying the variables, formulate the profit function that needs to be solved.[3 marks]
  2. 1(a)(ii)a)On the graph sheet provided, draw the graphs of the inequalities obtained in (i) b).[6 marks]
  3. 1(a)(ii)b)Identify the feasible region to solve the problem.[2 marks]
  4. 1(a)(iii)a)From your graph, determine the number of EACH type of bottle required for maximum profit.[3 marks]
  5. 1(a)(iii)b)Determine the maximum profit.[2 marks]
  6. 1(b)Determine the SHORTEST and LONGEST path from Town S to Town G.[2 marks]

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