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Linear Models and Inventory Sampling.

All 3 questions please.

Background (This case was taken from an article that appears in The Economist Dec. 2020) Barilla Pasta is the largest pasta maker in the world. The organization has a modern high-tech facility located at its world headquarters in Parma, Italy. Barilla exports 60% of its products; mainly to Europe and the U.S. Because of the COVID pandemic, people around the world are staying home and cooking for themselves. As a result, pasta sales world wide has increased. Likewise, pasta sales for Barilla has increased around 30% from 2019 to 2020. One of Barilla's most important markets is Germany. Since March of 2020, Barilla has supplied 22% of the pasta and 39% of the pasta sauces and pestos eaten in Germany (The Economist, Dec. 2020). Global sales for Barilla were $4.2 billion for 2019. The Problems Because of the international growth in pasta sales, Barilla may be experiencing problems with its hourly production capacity and its rail (train) shipments. You are an executive with Barilla and you are a member of a team responsible for inventory and supply chains. You need to evaluate whether to focus your attention on hourly production capacity or rail car shipments as a way to increase revenue streams. 1. Barilla has a total demand per shipment of $22,982 per day, and revenue (sales) per ton shipment for pasta (X) is $11,497. The revenue per ton shipment for the pasta sauce and pesto (X) is $11,485. Also, the production capacity that Barilla has available is 25 tons per hour. It takes 20 tons of capacity per hour to produce pasta and 4.58 tons of capacity per hour to produce the pasta sauces. Develop a linear program that will maximize the following daily revenue streams for Barilla, given that $5,633,753 is the daily revenue per shipment of pasta to Germany and $1,263,452 is the daily revenue for the sauces shipped to Germany. Note: The first problem involves managing the limited hourly production capacity while maximizing revenue per shipment. The second problem involves managing the rail (train) car limitations for shipping while maximizing revenue. 2. Managing the shipments to Germany from Italy is also a major problem. If the shipments are mismanaged, losses will result. This problem is a continuation of the previous problem. The objective function and the first constraint in the previous problem remain the same. The total number of rail cars available per shipment to Barilla is 16. The pasta load takes 13 rail cars per shipment. The sauce and pesto load takes approximately 2.93 train cars per shipment. Rerun the previous linear program to determine which approach to managing the problem will yield the best results. 3. To provide extra depth to your analyses, you decide to also provide to your bosses with an inventory study of the problem. Given that demand in Germany for pasta is 490 tons per day and demand for sauce and pesto is 110 tons a day, the holding cost rate is 7%, the ordering cost is $500 per order, the cost for pasta is $413,892 per shipment per year, the cost for sauce and pesto is $411,460 per shipment per year, the working days are 363 and the lead time is 3 shipments per week (7 day work week), perform following analyses: a) EOQ model; b) Reorder Point; c) Cycle Time: and d) Total Inventory Costs for all information. Background (This case was taken from an article that appears in The Economist Dec. 2020) Barilla Pasta is the largest pasta maker in the world. The organization has a modern high-tech facility located at its world headquarters in Parma, Italy. Barilla exports 60% of its products; mainly to Europe and the U.S. Because of the COVID pandemic, people around the world are staying home and cooking for themselves. As a result, pasta sales world wide has increased. Likewise, pasta sales for Barilla has increased around 30% from 2019 to 2020. One of Barilla's most important markets is Germany. Since March of 2020, Barilla has supplied 22% of the pasta and 39% of the pasta sauces and pestos eaten in Germany (The Economist, Dec. 2020). Global sales for Barilla were $4.2 billion for 2019. The Problems Because of the international growth in pasta sales, Barilla may be experiencing problems with its hourly production capacity and its rail (train) shipments. You are an executive with Barilla and you are a member of a team responsible for inventory and supply chains. You need to evaluate whether to focus your attention on hourly production capacity or rail car shipments as a way to increase revenue streams. 1. Barilla has a total demand per shipment of $22,982 per day, and revenue (sales) per ton shipment for pasta (X) is $11,497. The revenue per ton shipment for the pasta sauce and pesto (X) is $11,485. Also, the production capacity that Barilla has available is 25 tons per hour. It takes 20 tons of capacity per hour to produce pasta and 4.58 tons of capacity per hour to produce the pasta sauces. Develop a linear program that will maximize the following daily revenue streams for Barilla, given that $5,633,753 is the daily revenue per shipment of pasta to Germany and $1,263,452 is the daily revenue for the sauces shipped to Germany. Note: The first problem involves managing the limited hourly production capacity while maximizing revenue per shipment. The second problem involves managing the rail (train) car limitations for shipping while maximizing revenue. 2. Managing the shipments to Germany from Italy is also a major problem. If the shipments are mismanaged, losses will result. This problem is a continuation of the previous problem. The objective function and the first constraint in the previous problem remain the same. The total number of rail cars available per shipment to Barilla is 16. The pasta load takes 13 rail cars per shipment. The sauce and pesto load takes approximately 2.93 train cars per shipment. Rerun the previous linear program to determine which approach to managing the problem will yield the best results. 3. To provide extra depth to your analyses, you decide to also provide to your bosses with an inventory study of the problem. Given that demand in Germany for pasta is 490 tons per day and demand for sauce and pesto is 110 tons a day, the holding cost rate is 7%, the ordering cost is $500 per order, the cost for pasta is $413,892 per shipment per year, the cost for sauce and pesto is $411,460 per shipment per year, the working days are 363 and the lead time is 3 shipments per week (7 day work week), perform following analyses: a) EOQ model; b) Reorder Point; c) Cycle Time: and d) Total Inventory Costs for all information