7. A theatre company is planning to sell two types of ticket, standard and premier. The theatre company has completed some market research and has used this to form the following constraints.

• They will sell at most 450 tickets.
• They will sell at least three times as many standard tickets as premier tickets.
• At most \(85 \%\) of all the tickets sold will be standard.

The theatre wants to maximise its profit. The profit on each standard ticket sold is \(\pounds 5\) and the profit on each premier ticket sold is \(\pounds 8\)
Let \(x\) represent the number of standard tickets sold and \(y\) represent the number of premier tickets sold. Formulate this as a linear programming problem, stating the objective and listing the constraints as simplified inequalities with integer coefficients. You should not attempt to solve the problem.
(Total 6 marks)