5 Corey is training for a race that starts in 18 hours time. He splits his training between gym work, running and swimming.

• At most 8 hours can be spent on gym work.
• At least 4 hours must be spent running.
• The total time spent on gym work and swimming must not exceed the time spent running.

Corey thinks that time spent on gym work is worth 3 times the same time spent running or 2 times the same time spent swimming. Corey wants to maximise the worth of the training using this model.

1. Formulate a linear programming problem to represent Corey's problem. Your formulation must include defining the variables that you are using. Suppose that Corey spends the maximum of 8 hours on gym work.
2. 1. Use a graphical method to determine how long Corey should spend running and how long he should spend swimming.
   2. Describe why this solution is not practical.
   3. Describe how Corey could refine the LP model to make the solution more realistic.