Formulating linear programsEdexcel International A Level Maths: Mind map

Exam questions on Formulating linear programs

1. A bakery makes two types of bread. Each batch of loaf A needs 3 kg of flour and 2 hours of oven time. Each batch of loaf B needs 2 kg of flour and 4 hours of oven time. Each day there are 60 kg of flour and 80 hours of oven time available. The profit is £20 per batch of A and £30 per batch of B. The bakery makes $x$ batches of A and $y$ batches of B each day, and wants to maximise its daily profit.
   Write down the objective function, saying whether it is to be maximised or minimised, and write down the non-negativity conditions.2 marks
2. A farmer mixes two feeds, X and Y, for cattle. Feed X costs £0.40 per kg and contains 3 units of protein and 1 unit of vitamin per kg. Feed Y costs £0.60 per kg and contains 1 unit of protein and 2 units of vitamin per kg. Each day the mixture must provide at least 15 units of protein and at least 12 units of vitamin, and the farmer can store at most 20 kg of mixture. The farmer uses $x$ kg of X and $y$ kg of Y each day, and wants to minimise the daily cost.
   Write down the inequality for the vitamin requirement and the inequality for the storage limit.2 marks
3. A workshop makes $x$ tables and $y$ chairs each week. A table needs 6 hours of carpentry and 1 hour of painting. A chair needs 2 hours of carpentry and 1 hour of painting. There are 120 hours of carpentry and 40 hours of painting available each week. The workshop must make at least 4 tables and at least three times as many chairs as tables. The profit is £50 per table and £15 per chair, and the workshop wants to maximise its weekly profit. Only whole tables and chairs can be made.
   Write down the inequalities for the hours of carpentry and painting, and for the non-negativity of the variables.3 marks