Formulating linear programsEdexcel A-Level Further Maths: Mind map

Exam questions on Formulating linear programs

1. A workshop makes $x$ tables and $y$ chairs each week. Each table needs 3 hours of cutting time and each chair needs 2 hours. There are at most 20 hours of cutting time available each week.
   Find the value of $s_1$ when $x=4$ and $y=3$, and state what it represents in context.2 marks
2. A farmer mixes $x$ kg of feed A and $y$ kg of feed B. Each kilogram of either feed supplies 1 unit of a vitamin, and the mixture must supply at least 5 units of the vitamin in total.
   An artificial variable $t_1$ is also added to this constraint. Write down the equation and explain why $t_1$ is needed.2 marks
3. A company makes $x$ standard gift boxes and $y$ deluxe gift boxes each day. A standard box needs 4 minutes of packing and 2 metres of ribbon; a deluxe box needs 6 minutes of packing and 5 metres of ribbon. Each day there are 240 minutes of packing time and 150 metres of ribbon available, and at least 10 boxes must be made. Profit is £3 per standard box and £5 per deluxe box. The company wishes to maximise its daily profit $P$ (in pounds).
   Formulate this situation as a linear programming problem.3 marks