2 Codron Farm Case Melis Gn is a medium-sized farmer on his 500 decares of land in the north of Antalya. She has been in this market as a Codron Farm by expanding farm since 2018. It plans to plant wheat, barley, oats and rye in the coming season. The table below shows the estimated values for these products' yields, labor requirements, pre-harvest expenditures, water requirements other than rain, and sales prices. Wheat Barley Oats Rye Estimated Revenue (kg/decares) 525 750 450 600 Labor Requirement (hour/decares) 1 1,25 0,75 2,5 Pre-harvest Expenditures (TL/decares) 18 28 11 22 water requirements (ton/decares) 5 15 2,5 10 Sales Price (TL/decares) 0,48 0,39 0,215 0,455 Codron Farm expects to produce at least 80 tons of wheat and 80 tons of barley. The demand of oat in market has been decreasing year by yaer. Therefore, the maximum tons of oat to produce is 50 tons. The company has a budget of 16 thousand TL to spend on products throughout the year and will be able to work 9 hours a day during the 200-day product development period. It will be able to provide a total of 5000 tons of water throughout the year from the irrigation canal. . a) Write decision variables of the case and explain them in detail. You can see the example for definition of decision variable. By: amount of j brnad purchased at the beginning of the i time Vje B={Brand X, Brand Y), i E T={Time 1, Time 2, Time 3} b) Specify the chusters, indexes, objective function and parameters. Rename them to be used in mathe- matical model and gurohi parts. (Please explain each parameters by using its indexes, you can get help from the Lab Hour excel documents) . c) Write a mathematical programming model of the case. There is an example for the part b and c below. Cluster (Set): S: Source Cities Cluster (Des Moines, Evansville, Fort Lauderdale) D: Destination Cities Cluster { Albuquerque, Boston, Cleveland) Index: i: source type J: destination type Decision Variable: Xij: number of products transport from source i to destination Parameter: cost ij: unit cost of transportation from source i to destination supply the amount of products source i produced demand j: the amount of products demanded in destination Mathematical Model: Objective Function: Min Exj cost ij Constraints: { xij s supplyi Vies xij = demands Vied d) Please finds finds how many decares of which crop should be planted in order to maximize expected revenue of the company at the end of the harvest by using gurobi on excel. 2 Codron Farm Case Melis Gn is a medium-sized farmer on his 500 decares of land in the north of Antalya. She has been in this market as a Codron Farm by expanding farm since 2018. It plans to plant wheat, barley, oats and rye in the coming season. The table below shows the estimated values for these products' yields, labor requirements, pre-harvest expenditures, water requirements other than rain, and sales prices. Wheat Barley Oats Rye Estimated Revenue (kg/decares) 525 750 450 600 Labor Requirement (hour/decares) 1 1,25 0,75 2,5 Pre-harvest Expenditures (TL/decares) 18 28 11 22 water requirements (ton/decares) 5 15 2,5 10 Sales Price (TL/decares) 0,48 0,39 0,215 0,455 Codron Farm expects to produce at least 80 tons of wheat and 80 tons of barley. The demand of oat in market has been decreasing year by yaer. Therefore, the maximum tons of oat to produce is 50 tons. The company has a budget of 16 thousand TL to spend on products throughout the year and will be able to work 9 hours a day during the 200-day product development period. It will be able to provide a total of 5000 tons of water throughout the year from the irrigation canal. . a) Write decision variables of the case and explain them in detail. You can see the example for definition of decision variable. By: amount of j brnad purchased at the beginning of the i time Vje B={Brand X, Brand Y), i E T={Time 1, Time 2, Time 3} b) Specify the chusters, indexes, objective function and parameters. Rename them to be used in mathe- matical model and gurohi parts. (Please explain each parameters by using its indexes, you can get help from the Lab Hour excel documents) . c) Write a mathematical programming model of the case. There is an example for the part b and c below. Cluster (Set): S: Source Cities Cluster (Des Moines, Evansville, Fort Lauderdale) D: Destination Cities Cluster { Albuquerque, Boston, Cleveland) Index: i: source type J: destination type Decision Variable: Xij: number of products transport from source i to destination Parameter: cost ij: unit cost of transportation from source i to destination supply the amount of products source i produced demand j: the amount of products demanded in destination Mathematical Model: Objective Function: Min Exj cost ij Constraints: { xij s supplyi Vies xij = demands Vied d) Please finds finds how many decares of which crop should be planted in order to maximize expected revenue of the company at the end of the harvest by using gurobi on excel