Problem se (50 points) (No credits for just answers without showing the worki S, show you worke) Suppose you are the manager of a farm that seeks a combination of crop and livestock activities that will maximize the total gross margin for a farm in 2021. Table B displays Gross margin for the different commodities Table B: Gross Margins per acre/head Year Cornacre) Wheet(a.cre) Soybeans acre) Horses head 2016 20 100 40 100 2017 30 120 35 50 2018 80 100 150 160 2019 10 45 40 2020 70 200 250 and Table C the resource availability and requirements. Table C below shows the resource requirements per commodity (crop/livestock): Com (acre) Whent (nere) Soybeans (rare) Resource Horses (head) Resource endowment Hired Labor 1.3 14 2.000 hours Family Labor 0.5 03 05 0.4 500 hours Machine Time 2.2 2.1 3 1000 hours Land 0.4 1. 3 2600 acres How would you allocate the 2 600 acres of land if your objective is to maximize the total gross margin? What is the optimal level of gross margin? Would you use up all the available resources Why and explain? (20 2. Calculate the shadow price of each resource and interpret its significance. Get For your next planning season, will you increase the number of hired labor-hours? Why? What's about land if you could? Why? (points) 4 Compute the variance-covariance matrix associated with the total gross margin of these four commodities? (5 pts Use solver to calculate the minimum risk level associated with a portfolio constituted of all these resources if your objective is to obtain the optimal gross margin realized in ()? (15 ! What is the minimum risk if the objective is to realize a total gross margin that is 5% less than the one obtained in (0)7 Gets! 5 6. Problem se (50 points) (No credits for just answers without showing the worki S, show you worke) Suppose you are the manager of a farm that seeks a combination of crop and livestock activities that will maximize the total gross margin for a farm in 2021. Table B displays Gross margin for the different commodities Table B: Gross Margins per acre/head Year Cornacre) Wheet(a.cre) Soybeans acre) Horses head 2016 20 100 40 100 2017 30 120 35 50 2018 80 100 150 160 2019 10 45 40 2020 70 200 250 and Table C the resource availability and requirements. Table C below shows the resource requirements per commodity (crop/livestock): Com (acre) Whent (nere) Soybeans (rare) Resource Horses (head) Resource endowment Hired Labor 1.3 14 2.000 hours Family Labor 0.5 03 05 0.4 500 hours Machine Time 2.2 2.1 3 1000 hours Land 0.4 1. 3 2600 acres How would you allocate the 2 600 acres of land if your objective is to maximize the total gross margin? What is the optimal level of gross margin? Would you use up all the available resources Why and explain? (20 2. Calculate the shadow price of each resource and interpret its significance. Get For your next planning season, will you increase the number of hired labor-hours? Why? What's about land if you could? Why? (points) 4 Compute the variance-covariance matrix associated with the total gross margin of these four commodities? (5 pts Use solver to calculate the minimum risk level associated with a portfolio constituted of all these resources if your objective is to obtain the optimal gross margin realized in ()? (15 ! What is the minimum risk if the objective is to realize a total gross margin that is 5% less than the one obtained in (0)7 Gets! 5 6
