Linear Programming (LP) problems (Edexcel A Level Further Maths: Decision Maths 1)

Ben is a wedding planner. He needs to order flowers for the weddings that are taking place next month. The three types of flower he needs to order are roses, hydrangeas and peonies.

Based on his experience, Ben forms the following constraints on the number of each type of
flower he will need to order.

• At least three-fifths of all the flowers must be roses.
• For every 2 hydrangeas there must be at most 3 peonies.
• The total number of flowers must be exactly 1000

The cost of each rose is £1, the cost of each hydrangea is £5 and the cost of each peony is £4

Ben wants to minimise the cost of the flowers.

Let represent the number of roses, let represent the number of hydrangeas and let represent the number of peonies that he will order.
Formulate this as a linear programming problem in and only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients.

Ben decides to order the minimum number of roses that satisfy his constraints.