8. Class 8 B has decided to sell apples and bananas at morning break this week to raise money for charity. The profit on each apple is 20 p , the profit on each banana is 15 p . They have done some market research and formed the following constraints.

• They will sell at most 800 items of fruit during the week.
• They will sell at least twice as many apples as bananas.
• They will sell between 50 and 100 bananas.

Assuming they will sell all their fruit, formulate the above information as a linear programming problem, letting \(a\) represent the number of apples they sell and \(b\) represent the number of bananas they sell. Write your constraints as inequalities.
(Total 7 marks)