3. (30 pts.) Marsh and Sons Inc. are planning their daily production of two popular products P1 and P2 for the coming Christmas season. Labor minutes required for the Assembly and Packaging, as well as the Profit per unit are given in the table below: Time (minutes) P1 P2 45 5 $90 Assembly 15 Packaging 5 Unit Profit $60 Available 90 20 a. Formulate the LP problem. Write the Dual LP formulation then solve using the Dual- Simplex Method. b. How much is the contribution of each Assembly minute to the profit? c. How much is the contribution of each Packaging minute to the profit? d. What is the range of optimality for the unit profit of P1 only if the profit for P2 remains constant? For the unit profit of P2 only if the profit for P1 remains constant? e. What optimal solution changes will occur if the available Assembly and Packaging minutes increase to 120 and 30 minutes respectively?