GAMS exercises

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Exercise 1 – farming A farmer possesses a finite amount of land and labor and can access three types of crops. Each type of crop requires the same amount of land but a different amount of labor input and is sold at a different price. What is the optimal production decision for the farmer (i.e. revenue maximization) given the following data? Crops -> corn, wheat, cotton Prices -> 109, 90, 115 Labor -> 6,4,8 Max labor -> 500 Max land -> 100 Things you learned: sets, parameters, equations, summation over sets , model statement, solve statement, gdx generation Exercise 1.1 – add a constraint on crop production Now assume that the maximum production for wheat production is 10. How do the results change? Go check the marginal value for wheat production. Why is it non-zero? Things you learned: level, lower bound, upper bound, marginal. Exercise 1.2 – add explicit production costs and demand elasticity Now assume that the specific cost of land and labor is different and takes values of 10 and 5, respectively. Also, assume that the demand for the crops is elastic, i.e. the higher the quantity consumed, the lower the price consumers are willing to pay for it. Assume that the price decreases linearnly with demand. Initial values are equal to the price in the previous exercise, and slopes are given by: Crops -> corn, wheat, cotton Prices -> 109, 90, 115 Slopes -> 0.5,0.5,0 Maximize the profit for the farmer. How did the solution change? Things you learned: set depend ent equations, mind division by zero errors, fixed variables vs parameters, solve multiple models in a single file, nonlinear problems. Exercise 2 – transport problem We must decide the optimal trade allocation that maximizes total surplus. There are six cities: seattle, san- diego, new-york, chicago, topeka Some of…