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5 marksLinear Programming

CAPE Applied Mathematics Unit 2 · 2017 · Paper 2 · Question 1(a)(i)

A farmer has 50 acres for planting alfalfa and corn. Seed costs are 60/acre for alfalfa and 45/acre for corn. Labour costs are 40/acre for alfalfa and 80/acre for corn. Budget limits: at most 2700 for seeds and 3200 for labour. Income per acre: 110 for alfalfa and 150 for corn.

Using x for the number of acres of alfalfa and y for the number of acres of corn, formulate a linear programming problem and state clearly the maximizing function.

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Other parts of this question

  1. 1(a)(ii)On the grid provided, draw all lines defined by the constraints and shade the feasible region satisfying all constraints.[8 marks]
  2. 1(a)(iii)Determine the number of acres of alfalfa and the number of acres of corn that the farmer must plant to maximize income.[6 marks]
  3. 1(b)Write the contrapositive of p \rightarrow \sim q.[2 marks]
  4. 1(c)(i)List the vertices that have a degree greater than 2.[2 marks]
  5. 1(c)(ii)List all the paths from C to E.[2 marks]

More practice: the rest of this paper · more Linear Programming questions · all CAPE Applied Mathematics Unit 2 past papers