answer pasta question base on question 1

Question 1. Rutgers Business School is planning to open New Pasta Cafeteria. They are planning to serve several different types of pasta. After the survey from our students, Rutgers gets 5 candidates for its menu. However, each pasta needs different ingredients. The table below summarizes the ingredients required by each bowl of pasta, and the total capacity available for each ingredient. There is also a Recipe cost for each pasta that RBS has to pay to the chef. The table also shows you the unit profit for each pasta RBS wants to determine the most profitable mix of pastas to sell. Ingredient Pasta1 Pasta 2 Pasta 3 Pasta 4 Pasta 5 Supply Capacity (m) 2,000 3 0 2 3 1420 20 5.000 Mushroom Carrot Cabbage Price/bowl Recipe Cost 1,200 $18 $25 $20 $15 $600 $13 $900 $800 $1,500 $1,200 (A) Define Decision Variables, (5pts) X; = Open Number of Parta i=1,2,3,4,5 to lice open. Yi= 1 if pasta i=1,2,3,4,5 is planned to be sense o otherwise (B) Find Objective Function. (5pts) ) Max Z= 15 X + 18X2 + 25x + 13 X4 +2005 - 6001 - 8002-250 - 900 Yu - 120045 (C) Write Constraints and complete your modeling formulation. (20pts) *Due to limited number of workers in cafeteria, the cafeteria can only choose at most 4 menus (different pasta) to sell; however, also has to choose at least 2 menus to satisfy students demand. Y + Y tl z + Yu + Ys 24 Page 2 of 9 *Pasta & Pasta are both cream pastas, so if Pasta 1 is selected than Pasta 2 should be selected to simplify the process. Y, L / *Pasta 3 & Pasta 5 are both banana pastas, so if Pasta 3 is selected than Pasta 5 should not be selected to keep diversity. Y + Ye LiX * In addition, the instructor Kim wants to cat at least 1 menu among pasta 3,4, and 5. Yt Yu + Y Z 1 RBS is confident of this pasta restaurant. Therefore, when RBS decides to sell any pasta, RBS will make at least 300 bowls. However, because of market status, the expected demand for each product to be less than 500 bowls. Xi >3004 X 25oot (Extra) What happen if RBS finds one more chef and now considering extra Recipe, too. The below table is about the Recipe Cost for each pasta. (Extra bonus 5pts) Pasta 1 $700 Pasta 2 $1,000 Pasta 3 $1,200 Pasta 5 2nd Recipe Cost Pasta 4 $750 Then what will happen to your Decision Variables & Objective Function & Constraints. ST OBJECTIVE FUNCTION Max 2 = 15X1 +18X2 +25X2 + 1344 +2048-6004 -800Y - 15001 - 900 Y4 - 1200 Ys - 70029-10002 12002; -750 Z4 - 1100 Zs Constraights all on Back Pg. Page 3 of 9