Lesson Objective Revise Inequalities from GCSE Look at linear programming

1) Show the region satisfied by2) 3) 3y + x>12 2x + y ≤ 10 4y + 6x ≥ 12 x+y 1 x + y < 8 y ≤ 2x y < x 0<x ≤2

1) In a maths class there are less than 31 students. There are more than 20 girls. The number of girls is fewer than 3 times the number of boys. There are less than 10 boys. a) Write down 4 inequalities for this situation. b) Plot the inequalities and decide how many boys and girls there might be in the class. 2) A smallholder keeps ‘s’ sheep and ‘p’ pigs. Write each of these statements as an inequality in terms of ‘p’ and ‘s’. a)He has housing for only 8 animals b)He must have at least 2 pigs to keep each other company c)He needs at least three sheep to keep the grass short d)His wife prefers sheep and says that sheep must outnumber pigs. Show these inequalities on a graph using s for the horizontal axis. Use the graph to show all the combinations of pigs and sheep that are possible.

3) Anisa is buying apples and bananas for the tennis club picnic and she has £4 to spend. Apples cost 24p each and bananas 20p each. She must buy at least 18 pieces of fruit and she would like to buy at least 6 apples and at least 8 bananas. She buys ‘a’ apples and ‘b’ bananas Write down 4 inequalities to describe this situation and use a graph to find the possible combinations of fruit that she can buy. 2) A smallholder keeps ‘s’ sheep and ‘p’ pigs. Write each of these statements as an inequality in terms of ‘p’ and ‘s’. a)He has housing for only 8 animals b)He must have at least 2 pigs to keep each other company c)He needs at least three sheep to keep the grass short d)His wife prefers sheep and says that sheep must outnumber pigs. Show these inequalities on a graph using s for the horizontal axis. Use the graph to show all the combinations of pigs and sheep that are possible.

A linear programming task consists of a set of inequalities (usually described using words) that need to be satisfied and an objective function which needs to be met. Eg A factory produces two types of drink, an energy drink and a refresher drink. The day’s output is to be planned, so as to maximise the income from the drinks, assuming that all are sold. Each drink requires the same three ingredients, but mixed in different quantities, these are described in the table below: SyrupVitamin supplement Concentrated flavouring 5 litres of energy drink 1.25 litres2 units30 cc 5 litres of refresher drink 1.25 litres1unit20 cc Availabilities250 litres300 units4.8 litres The energy drink sells for £1 per litre and the refresher drink for 80p per litre.

Eg A factory produces two types of drink, an energy drink and a refresher drink. The day’s output is to be planned, so as to maximise the income from the drinks, assuming that all are sold. Each drink requires the same three ingredients, but mixed in different quantities, these are described in the table below: SyrupVitamin supplement Concentrated flavouring 5 litres of energy drink 1.25 litres2 units30 cc 5 litres of refresher drink 1.25 litres1unit20 cc Availabilities250 litres300 units4.8 litres The energy drink sells for £1 per litre and the refresher drink for 80p per litre.

SyrupVitamin supplement Concentrated flavouring 5 litres of energy drink 1.25 litres2 units30 cc 5 litres of refresher drink 1.25 litres1unit20 cc Availabilities250 litres300 units4.8 litres The energy drink sells for £1 per litre and the refresher drink for 80p per litre.