1. Green Inc. is a social impact startup that wants to sell fresh produce from three farmers, U, V and W in local markets. There are 2 markets, CA and NY in the vicinity that they consider. Price and capacity of the two markets are given in Table 1 below. The total quantity they sell in a market cannot exceed the capacity of the market. Green Inc. has contractual obligations that require it to sell all the fresh produce produced by farmers. Table 2 has data on the quantity produced by farmers. Green Inc's objective is to maximize the total revenue for farmers. Table 1: Market CA NY Price (per kg.) 20 40 Capacity (in kg.) 30 5 Table 2: Farmer U V W Production (in kg.) 10 20 5 a. Formulate the optimization problem and clearly specify the decision variables, objective function and constraints. b. Is the given problem feasible? If yes, give a feasible solution and show that it is feasible? c. The capacity of Market CA is reduced due to a cyclone and is only 20 kg now. Is this problem still feasible? If yes, show how. Otherwise, show why it is not feasible. d. Since Green Inc. is making a loss in transporting the produce to NY, it decides to charge a commission of 5% on revenue from sales in NY. It wants to ensure that the total commission earned is at least $30. How can you update the optimization formulation to account for this commission? 1. Green Inc. is a social impact startup that wants to sell fresh produce from three farmers, U, V and W in local markets. There are 2 markets, CA and NY in the vicinity that they consider. Price and capacity of the two markets are given in Table 1 below. The total quantity they sell in a market cannot exceed the capacity of the market. Green Inc. has contractual obligations that require it to sell all the fresh produce produced by farmers. Table 2 has data on the quantity produced by farmers. Green Inc's objective is to maximize the total revenue for farmers. Table 1: Market CA NY Price (per kg.) 20 40 Capacity (in kg.) 30 5 Table 2: Farmer U V W Production (in kg.) 10 20 5 a. Formulate the optimization problem and clearly specify the decision variables, objective function and constraints. b. Is the given problem feasible? If yes, give a feasible solution and show that it is feasible? c. The capacity of Market CA is reduced due to a cyclone and is only 20 kg now. Is this problem still feasible? If yes, show how. Otherwise, show why it is not feasible. d. Since Green Inc. is making a loss in transporting the produce to NY, it decides to charge a commission of 5% on revenue from sales in NY. It wants to ensure that the total commission earned is at least $30. How can you update the optimization formulation to account for this commission
