McOrange Inc. produces orange juice from three different grades of oranges. Oranges are graded 1(poor), 2 (medium), 3 (good) depending on their quality. The company produces three different types of orange juice (OJ) from these oranges: Superior, Premium and Regular. The demand of each orange juice type is unlimited (whatever can be produced, can be sold accordingly). 

Each juice type requires a minimum average grade and minimum daily production amount (in liters) which are given in the table above. On the other hand, the amount of juice obtained from each grade of orange and their current stock levels are given. The aim is to maximize the total profit of McOrange Inc. while meeting all the production requirements. 

(a) Formulate the problem as an LP. Clearly define your decision variables, objective function and the constraints. Do not forget the sign restrictions if there are any.

 (b) Solve the problem by using IBM ILOG CPLEX Optimization Studio. Write down the optimal solution. Define which constraint(s) is/are active (binding) at the optimal solution.

Grade Juice (It/kg) Current Stock (kg) 1 (Poor) 0.4 100 2 (Medium) 0.5 150 3 (Good) 0.6 200