Problem

A restaurant sells two sizes of pizza, small and large. The restaurant owner knows that, each evening, she needs to make

• at least 85 pizzas in total
• at least twice as many large pizzas as small pizzas

In addition, at most 80% of the pizzas must be large.

Each small pizza costs £2 to make and each large pizza costs £3 to make.

The restaurant owner wants to minimise her costs.

Let $x$ represent the number of small pizzas made each evening and let $y$ represent the number of large pizzas made each evening.

Formulate the information above as a linear programming problem. State the objective and list the constraints as simplified inequalities with integer coefficients. You should not attempt to solve the problem.

(Total 5 marks)