4. Palouse Grains & Legumes, Inc. (PGL) is trying to determine its crop rotation schedule for the next four years. Despite thec The crops available to plant are chickpeas, lentils, spring and winter wheat (combined for orporate-sounding name, P GL is a 160-acre family farm. convenience), and alfalfa. The following table provides average yields and prices: Crop Chickpeas Average yield (units/acre) 1.750 lbs. 1,500 lbs. 129 bushels 170 bushels Average price (per unit) $0.38/1b. $0.39/1b S4.38/bushel S3.90/bushel Wheat, combined Alfalfa Under the most simplistic interpretation, PGL would just choose the most profitable crop and plant it every year. However, agricultural decision order to ensure long-term soil quality, etc, farms must allow each acre to go fallow (unplanted) every few years in PGL's case, every fourth year for each acre). In other words, s are far more complicated than that. In both crop types and fallow years must be included in the crop rotation schedule. PGL must rotate crops so that the same crop is never planted in two consecutive years on a given acre. Additionally, to reduce risk and smooth consumption, PGL would like to earn a similar profit each year (so they can't let all acres go fallow in a single year, even if that would be the most profitable long-run option). There is some uncertainty associated with each crop's production, but we will ignore that for now. Using the information provided, answer the ucstions: a) What are the decision variables in this problem? Explain them carefully. [Hint: There can be more than 20 depending on how you set up the problem, but you may be able to explain them in groups.] b) Write out the objective function c Explain the constraints you would need (in words, at least) d) Can we solve this problem using the lincar programming approach? Explain your answer. 4. Palouse Grains & Legumes, Inc. (PGL) is trying to determine its crop rotation schedule for the next four years. Despite thec The crops available to plant are chickpeas, lentils, spring and winter wheat (combined for orporate-sounding name, P GL is a 160-acre family farm. convenience), and alfalfa. The following table provides average yields and prices: Crop Chickpeas Average yield (units/acre) 1.750 lbs. 1,500 lbs. 129 bushels 170 bushels Average price (per unit) $0.38/1b. $0.39/1b S4.38/bushel S3.90/bushel Wheat, combined Alfalfa Under the most simplistic interpretation, PGL would just choose the most profitable crop and plant it every year. However, agricultural decision order to ensure long-term soil quality, etc, farms must allow each acre to go fallow (unplanted) every few years in PGL's case, every fourth year for each acre). In other words, s are far more complicated than that. In both crop types and fallow years must be included in the crop rotation schedule. PGL must rotate crops so that the same crop is never planted in two consecutive years on a given acre. Additionally, to reduce risk and smooth consumption, PGL would like to earn a similar profit each year (so they can't let all acres go fallow in a single year, even if that would be the most profitable long-run option). There is some uncertainty associated with each crop's production, but we will ignore that for now. Using the information provided, answer the ucstions: a) What are the decision variables in this problem? Explain them carefully. [Hint: There can be more than 20 depending on how you set up the problem, but you may be able to explain them in groups.] b) Write out the objective function c Explain the constraints you would need (in words, at least) d) Can we solve this problem using the lincar programming approach? Explain your
