Problem 1 Muffy Bakery produces blueberry and carrot muffins. The demand for muffins, which must be met in time, are given below. It cost $0.65 to bake a blueberry and $0.55 carrot muffin. It costs $0.15 to hold a blueberry muffin, and $0.12 to hold a carrot muffin in inventory for a month. Muffy would like to have at least a dozen of each type of muffins in inventory at the end of month 3. Assume there are 5 blueberry and 0 carrot muffins in inventory at the beginning of month 1. Baking the muffins requires the use of the baking oven. Each blueberry muffin requires 0.1 hour baking time and carrot requires 0.14 hour. During each month, there is 135 hours available. The muffins don't do well in storage and 10% of the inventory is spoiled and cannot be used to service demand for the next month. Muffins Blueberry Carrot Month 1 400 420 Month 2 300 320 Month 3 200 220 (a) Formulate a LP model to minimize the total cost of meeting the next three month's demand. (a) Formulate a LP model to minimize the total cost of meeting the next three month's demand. Solve the model using LINGO and provide the minimum cost. You can leave answer as fraction. (10 marks) (b) Last month, Muffy made a total of 400 muffins. The union will not allow the total number of muffins made increase or decrease by more than 150 units from month to month. What changes will you need to make to the model in (a)? You do not have to solve this part in LINGO. (3 marks)