3. A ball point pen manufacturing company makes three models of ball point pens. Requirements for each lot of pens for each model are given below. Economy Model Super Model Premium Model Available Plastic 3 4 4 800 units Ink Assembly Molding Time 3 4 6 1120 units 4 3 8 1200 hours The profit for the economy model is $900 per lot. The profit for the super model is $1150 per lot and the profit for the premium model is $1600 per lot. How many lots of each model should the company manufacture to maximize the total profit? (a) Formulate a linear optimization model for this problem. (b) Solve this model by using the Excel Solver. Include Excel output with your answer. (c) Determine the optimal solution. Interpret and make recommendations based on the optimal solution.