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3 marksLinear Programming

CSEC Mathematics · May/June 2012 · Paper 2 · Question 9(b)(iv)

A florist makes bouquets of flowers, each consisting of x roses and y orchids. The constraints are: the number of orchids must be at least half the number of roses; there must be at least 2 roses; there must be no more than 12 flowers.

The florist sells a bouquet of flowers to make a profit of 3 on each rose and 4 on each orchid. Determine the MAXIMUM possible profit on the sale of a bouquet.

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Other parts of this question

  1. 9(a)(i)Solve the pair of simultaneous equations: y = 8 - x and 2x² + xy = -16.[5 marks]
  2. 9(a)(ii)State, giving the reason for your answer, whether the line y = 8 - x is a tangent to the curve 2x² + xy = -16.[2 marks]
  3. 9(b)(i)Write THREE inequalities for the constraints given.[3 marks]
  4. 9(b)(ii)On the answer sheet provided, shade the region of the graph which represents the solution set for the inequalities in (b)(i).[1 mark]
  5. 9(b)(iii)State the coordinates of the points which represent the vertices of the region showing the solution set.[1 mark]

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