4. (25 points) Consider a supply chain network with three potential sites for warehouses and five retailer regions. The fixed costs of building warehouses at the three sites are given as follows: Sitel: $100,000 Site2: $90,000 Site3: S120,000 The capacity of each warehouse is 3000, 2800, 4000, respectively. The retailer demands are given as: RI R2 R3 R4 RS Demand 900 700 1200 1100 950 R3 R4 R5 The unit transportation costs are given in the table below: Ri R2 Site1 5 4 Site2 3 5 4 Site3 3 7 5 6 7 Notably, the company plans to select at least two sites for warehouses. Formulate a mixed integer model to determine the optimal location and distribution plan so that the total cost is minimized. Please clearly define the decision variable(s), list the constraints, and formulate the objective function. Bonus question (10 points) Jason & Sons, a manufacturer of exercise equipment is investigating the possibility of expanding the business over the next 3 years. Undertaking this project will require either moving to a new site now or expand store at the current site now. Also, the company has the option of do nothing and reconsider the expansion option (at the current site) one year later if a strong growth is observed. The demand will be of strong growth with a probability of 0.6 and of a weak growth with a probability of 0.4. Move to the new site would cost $200,000 and expansion at the current site only costs $90,000 (do nothing costs So). The annual return of the company depends on the owner's decision and the demand realization: Annual Return Strong growth Weak growth Move $190,000 $112,000 Owner's Decision Expand $175,000 $100,000 Do nothing $160,000 S105,000 Draw the decision tree, show the stand and slanul stata una conclurinn