POM, Assignment 3 Question 1 Trader ZZOE would like to open a bubble tea delivery business near Rutgers Business School. It is thinking to sell 4 different flavors. After the survey of our students, ZZOE gets 4 candidates for its menu. No matter what flavor it sells, each must undergo brewing, stirring, and packaging. The table below summarizes the minutes of brewing, stirring, and packaging required by each unit of bubble tea. In addition, you have total hours of capacity available for each work. The company wants to determine the most profitable mix of products to sell; however, it realizes some restrictions that it needs to consider. Flavor 1 Flavor 2 Flavor 3 Flavor 4 Available (Hours) Brewing 3 1 5 9 10 Stirring 2 2 3 12 Packaging 4 7 4 15 Unit Profit $4 $5 $7 $8 Fixed Cost $800 $700 $650 $800 The unit profit and the setup cost for each bubble tea are provided in the table above. The fixed cost only occurs when the flavor is selected to produce. Considering the variability of choice, the company must sell at least two different flavors. Flavors 3 and 4 use the same ingredients, so if flavor three is selected, then flavor four must be selected to simplify the supply chain. If the company decides to produce any product, it must make at least 70 units of that product. The marketing department expected the demand for each flavor to be less than 400 units. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints. d. Use 'Excel - Solver' and find the optimal solution. (You must submit your excel work to get the full points.)Question 2 Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation costs and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of > or 10 million. Demand Region Production and Transportation Cost per Low Capacity High Capacity 1,000,000 Units North South South Fixed Capacity Fixed Capacity Supply Region America America Asia Europe Cost Cost North America 40 45 51 65 3000 4500 10 South America 51 47 60 3200 4800 10 South Asia 58 63 45 2000 3000 10 Europe 71 50 51 53 1800 2700 10 Demand 6 Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Your definition must include unit size & time frame. b. Develop the Objective Function. c. Find the constraints. d. Use 'Excel - Solver' and find the optimal solution. (You must submit your excel work to get the full points.)Question 3 Kim finally got his own baking factory. However; he found that the factory is too oily. He decides to hire cleaning teams and gures out that there are 4 sections to be cleaned. Each section can only be cleaned by one team. For each team, you must pay 'Contract Payment= for the regular workday. Once the cost is paid, each team can clean up to the following amount of area. Team 1: 150 [t2 Team 2: 120 it? Team 3: 170 [t2 Team 4: 80 {t2 In addition; if you pay the Contract payment, you may also pay Overtime Work Payment, and each team can clean up to an extra 30 t2. On the other hand: if you do not pay Contract Payment, you can't ask for overtime. The costs are as follows, Contract Payment I Overtime Work Payment Team 1 S 900 S 350 Team 2 1000 240 Each team estimates the area of the sections by its own way. The f_t2 of each section that each team estimate to clean is as follows: I I Section | Section 2 I Section 3 I Section 4 "ream I 22 16 3| 9 mm "earn 3 24 lg 25 10 Team 4 25 16 30 7 Kim wants to clean every section of his baking factog 1with minimum cost. a. Define Decision Variables. Your denition must include unit size & timfmme. b. Develop the Objective Function