7. Emily is planning to sell three types of milkshake, strawberry, vanilla and chocolate. Emily has completed some market research and has used this to form the following constraints on the number of milkshakes that she will sell each week.

• She will sell fewer than 200 non-vanilla milkshakes in total.
• She will sell at most 2.5 times as many strawberry milkshakes as vanilla milkshakes.
• At most, \(75 \%\) of the milkshakes that she will sell will be vanilla.

The profit on each strawberry milkshake sold is \(\pounds 0.75\), the profit on each vanilla milkshake sold is \(\pounds 1.20\) and the profit on each chocolate milkshake sold is \(\pounds 1.45\) Emily wants to maximise her profit.
Let \(x\) represent the number of strawberry milkshakes sold, let \(y\) represent the number of vanilla milkshakes sold and let \(z\) represent the number of chocolate milkshakes sold.

1. Formulate this as a linear programming problem, stating the objective and listing the constraints as simplified inequalities with integer coefficients. In week 1, Emily sells 100 strawberry milkshakes and 25 chocolate milkshakes.
2. Calculate the maximum possible profit and minimum possible profit, in pounds, for the sale of all milkshakes in week 1. You must show your working.