7. A caterer can make three different sizes of salad; small, medium and large. The caterer will make a total of at least 280 salads. The caterer wants at least \(35 \%\) of the salads to be small and no more than \(20 \%\) of the salads to be large. The caterer has enough ingredients to make 400 small salads or 300 medium salads or 200 large salads. The profit on each small, medium and large salad is \(40 \mathrm { p } , 60 \mathrm { p }\) and 85 p respectively. The caterer wants to maximise his total profit. Let \(x\) represent the number of small salads, \(y\) represent the number of medium salads and \(z\) represent the number of large salads. Formulate this information 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 8 marks)