Linear Programming question

Question 1: Linear Programs [12 points] The solution should include a brief description of all decision variables (state the meaning of each one). (a) OttawaDairy buys milk and produces cheese and butter. It owns a storage tank with a capacity of 10,000 litres, that initially contains 5,000 litres of milk. To produce one kilogram of cheese OttawaDairy needs 4 litres of milk. To produce one kilogram of butter OttawaDairy needs 5 litres of milk. OttawaDairy can sell up to 9,000 kilograms of cheese and up to 6,000 kilograms of butter each month for the next 3 months, at a price of $60 per kilogram of cheese and $70 per kilogram of butter in the first month, $70 per kilogram of cheese and $80 per kilogram of butter in the second month, and $70 per kilogram of cheese and $90 per kilogram of butter in the third month. Moreover, OttawaDairy can purchase up to 8,000 liters of milk each month either for production during the same month or for storage for later use. The cost for milk bought is $1 per litre in the first month, $2 per litre in the second month, and $1 per litre in the third month. Milk can be left in the storage tank at the end of each month. OttawaDairy's goal is to maximize the profit. Formulate a Linear Program for Ot- tawaDairy, to determine the amount of milk to be purchased, sold and stored, the amount of cheese and butter to be produced for each of the three months to achieve the goal.(b) Let o be the optimal value of the constructed Linear Program. Suppose that, OttawaDairy has to minimize the total amount of cheese produced subject to the profit being equal to o and to respecting the requirements of part (a). Modify your LP formulation of part (a) in order to take into account the additional requirements. (Briefly explain any new variables, any new constraints, and any changes to the objective function.)