Question 4: Linear/Integer programming A ferry company is planning to replace its fleet with a combination of two types of ferry. Each ferry of type A costs 4M and is expected to make a profit of 3000 per month. Each ferry of type B costs 10M and is expected to make a profit of 2000 per month. The company can spend 50M. For the most popular routes only ferry of type B can be used as type A will be too small so at least 1 ferry of type B must be purchased. Each ferry of type A requires 6 hours of maintenance per month and each ferry of type B requires 7 hours of maintenance per month. The company has 60 hours of maintenance available each month. The company want to maximise their monthly profit. a) Formulate a mathematical programming problem to help the company decide how many if any of each type of ferry should be purchased. [25 marks] b) Solve the model to determine how many ferries of each type the company should purchase. [40 marks) c) Which constraints have slack? [10 marks] d) Modify your model from part a) to add the constraint that if any ferries of type A are purchased at least 3 must be purchased. Does this affect the solution that you found in part b)? [25 marks)