When using LP to optimize the quantities moved in a supply chain network from 1 single supplier to 2 plants to 2 distribution warehouses and to 3 markets (customers). 1. How many decision variables are needed for formulation? 2. Develop the objective function that minimizes the total cost of supplies, production, and distribution. 3. Write a constraint that limits the supplier capacity. 4. Write a constraint for limits the production capacity of the plants. 5. Write a constraint that limits the capacity of distribution warehouses. 6. Write a constraint that meets the demand of the customers. 7. Write a constraint that guarantees that the quantities shipped out of a warehouse cannot exceed the quantities received from the plants