Lesson Objective
Revise Inequalities from GCSE
Look at linear programming
1) Show the region satisfied by
3y + x>12
x+y<10
y ≤ 2x
2)
3)
2x + y ≤ 10
y>1
y<x
4y + 6x ≥ 12
x+y<8
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.
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.
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:
Syrup
5 litres of energy
drink
1.25 litres
Vitamin
supplement
Concentrated
flavouring
2 units
30 cc
5 litres of refresher
drink
1.25 litres
1unit
20 cc
Availabilities
250 litres
300 units
4.8 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:
Syrup
5 litres of energy
drink
1.25 litres
Vitamin
supplement
Concentrated
flavouring
2 units
30 cc
5 litres of refresher
drink
1.25 litres
1unit
20 cc
Availabilities
250 litres
300 units
4.8 litres
The energy drink sells for £1 per litre and the refresher drink for 80p per litre.
Syrup
5 litres of energy
drink
1.25 litres
Vitamin
supplement
Concentrated
flavouring
2 units
30 cc
5 litres of refresher
drink
1.25 litres
1unit
20 cc
Availabilities
250 litres
300 units
4.8 litres
The energy drink sells for £1 per litre and the refresher drink for 80p per litre.