Linear programming

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   A bakery makes $x$ trays of muffins and $y$ trays of cookies each day.

   • Each tray of muffins uses 2 kg of flour and 4 kg of sugar; each tray of cookies uses 3 kg of flour and 2 kg of sugar.
   • At most 120 kg of flour and 160 kg of sugar are available each day.
   • At least 10 trays of cookies must be made.
   • Profit is $5 per tray of muffins and $4 per tray of cookies.

   (a) Formulate this as a linear programming problem.

   (b) The vertices of the feasible region are $(0, 10)$, $(0, 40)$, $(30, 20)$ and $(35, 10)$. Find the number of trays of each type that maximises profit, and the maximum profit.

   Mark scheme

   • (a) Flour: $2x + 3y \le 120$ (1)
   • Sugar: $4x + 2y \le 160$, i.e. $2x+y\le 80$ (1)