Question 2: PastryPalace Bakeries is a newly established bakery chain specializing in pastries, operating in the state of California. PastryPalace is contemplating the establishment of bakeries in seven potential locations: Los Angeles, San Diego, San Jose, San Francisco, Fresno, Oakland, and Riverside. Each bakery can produce up to 900,000 pastries each year. The cost of establishing a PastryPalace at each site is ( $ 500,000 ) in Los Angeles, ( $ 400,000 ) in San Diego, ( $ 450,000 ) in San Jose, ( $ 300,000 ) in San Francisco, ( $ 475,000 ) in Fresno, and ( $ 450,000 ) in Oakland. Assume that once established, a PastryPalace lasts indefinitely. For simplicity, assume that PastryPalace has only 6 customers. The annual demand for each customer is as follows: 550,000 pastries for Customer ( 1 ; 500,000 ) pastries for Customer 2; 700,000 pastries for Customer 3; 650,000 pastries for Customer 4; 600,000 pastries for Customer 5; and 750,000 pastries for Customer 6 . For production, it is given that either San Diego or Fresno must produce a minimum of 800,000 pastries per year. Moreover, at least 150,000 units of the demand for customer 2 must be fulfilled from either Los Angeles or Riverside. There are additional constraints regarding the locations of establishments. Due to budget limitations and operational considerations, at most 5 bakeries can be established. If a bakery is established in Los Angeles, then one must also be established in San Diego. Furthermore, a bakery must be established either in San Francisco or Oakland. The total cost of baking and transporting a pastry to a customer is given in table below. a) Formulate a mixed-integer programming model that can be used to minimize the annual costs of meeting demand. Write down the mathematical model both in open form and closed form representation. b) Solve the problem using GAMS and answer the following questions: (i) Which bakeries should be opened? (ii) What is the number of products that is produced and transported from each location to each customer? (You must name the GAMS code as NameSurnameQ2.gms, and the PDF file that includes the mathematical model in both open and closed form representation as NameSurnameQ2.pdf. Do not upload. gsp files.)

Question 2: PastryPalace Bakeries is a newly established bakery chain specializing in pastries, operating in the state of California. Pastry Palace is contemplating the establishment of bakeries in seven potential locations: Los Angeles, San Diego, San Jose, San Francisco, Fresno, Oakland, and Riverside. Each bakery can produce up to 900,000 pastries each year. The cost of establishing a PastryPalace at each site is $500,000 in Los Angeles, $400,000 in San Diego, $450,000 in San Jose, $300,000 in San Francisco, $475,000 in Fresno, and $450,000 in Oakland. Assume that once established, a PastryPalace lasts indefinitely. For simplicity, assume that PastryPalace has only 6 customers. The annual demand for each customer is as follows: 550,000 pastries for Customer 1: 500,000 pastries for Customer 2; 700,000 pastries for Customer 3; 650,000 pastries for Customer 4; 600,000 pastries for Customer 5; and 750,000 pastries for Customer 6. For production, it is given that cither San Diego or Fresno must produce a minimum of 800,000 pastries per year. Moreover, at least 150,000 units of the demand for customer 2 must be fulfilled from either Los Angeles or Riverside. There are additional constraints regarding the locations of establishments. Due to budget limitations and operational considerations, at most 5 bakeries can be established. If a bakery is established in Los Angeles, then one must also be established in San Diego. Furthermore, a bakery must be established either in San Francisco or Oakland. The total cost of baking and transporting a pastry to a customer is given in table below. Customer 1 Customer 2 Customer 3 Customer 4 Customer 5 Customer 6 $12 $6 $11 $8 $7 $13 56 $13 SII $11 $14 $15 $8 $15 $16 $6 $7 $5 $10 FROM Los Angeles San Diego San Jose San Francisco Fresno Oakland Riverside $8 $9 $7 $14 $7 $9 $12 $8 $12 $13 $6 $13 $12 $14 $14 $13 $13 5.5 $14 $8 $12 $15 $7 a) Formulate a mixed-integer programming model that can be used to minimize the annual costs of meeting demand. Write down the mathematical model both in open form and closed form representation. b) Solve the problem using GAMS and answer the following questions: (1) Which bakeries should be opened? (ii) What is the number of products that is produced and transported from each location to each customer? (You must name the GAMS code as NameSurnameQ2.gms, and the PDF file that includes the mathematical model in both open and closed form representation as NameSurnameQ2.pdf. Do not upload. gsp files.)