(Solved) : Exercise 1 Population Equation Stochastic Simulation Matlab Programming Exercise 8 Pts Int Q37803464 . . .
EXERCISE 1: POPULATION EQUATION -STOCHASTIC SIMULATION (MATLAB PROGRAMMING EXERCISE; 8 PTS.) INTRODUCTION Parasitic nematode damage to wheat crops is estimated to cost approximately $157 billion worldwide [1]. While several methods have been proposed to control nematode infection of wheat, none are completely successful. In this problem we will explore the nematode control potential of two chemicals: chemical X and chemical Y. Each chemical has a different action mechanism, and the effectiveness of each varies with environmental conditions. There is also a cost difference between the two chemicals. PROBLEM STATEMENT Assume that a wheat field contains 2000 bushels of hard red winter wheat on 1 March 2017. Each week there is a 15% chance of rain, a 55% chance of clouds, and a 30% chance of sun. The wheat’s growth rate depends on the weather: 2.08% per rainy week, 1.75% per sunny week, and 0.75% per cloudy week. Parasitic nematode damage occurs at the end of each week, and, this damage is also dependent upon the weather (all damage/destruction of wheat occurs at the end of any week): 20 bushels of wheat are destroyed at the end of cloudy weeks, 25 bushels are destroyed at the end of rainy weeks, but 35 bushels are destroyed at the end of sunny weeks: Baseline Destruction of Wheat by Parasitic Nematodes SUNNY wEEK ! CLOUDY WEEK | RAINY WEEK 20 bushels NEMATODE DAMAGE 25 bushels 35 bushels The decision about whether to apply either Chemical X or chemical Y to the wheat field is made on 30 April 2017 (for Chemical X) or on 31 May 2017 (for Chemical Y); each chemical is effective until 31 August 2018, after which neither chemical is effective. Each week that a chemical is effective, it controls crop damage from parasitic nematodes, i.e., the destruction of wheat by nematodes is modified while a chemical is effective. The modification is also weather-dependent: Modified Destruction of Wheat by Parasitic Nematodes (per chemical) RAINY WEEK 10 bushels 2 bushels SUNNY WEEK CLOUDY WEEK 6 bushels 10 bushels 18 bushels 25 bushels CHEMICAL X CHEMICALY The hard red winter wheat from this field is harvested on 1 December 2017 PROBLEM SOLUTION REQUIREMENTS The solution to this problem shall consist of three separate parts, (A), (8) and (C), as described below. For each simulation in part (A), provide a screenshot displaying: the Matlab code for that simulation; the histogram from that simulation; the calculation of the mean harvest yield for that simulation (appearing in the command console window); the calculation of the standard deviation of the mean harvest yield for that simulation (also appearing in the command console window); AND HANDWRITTEN MATLAB CODE FOR ONE SIMULATION (your choice) (A) Conduct three separate simulations of the wheat field harvest yield eh 1 December 2017, as follows: Simulation 1: No chemicals are applied to the wheat field Simulation 2: Chemical X is applied to the wheat field on 30 April 2017 . .Simulation 3: Chemical Y is applied to the wheat field on 31 May 2017 Each simulation (Simulation 1, Simulation 2 and Simulation 3) shall consist of 100,000 model runs. That is, your model code will be executed 100,000 times. If you have questions about how to do this, refer to the example code “wheatfield3.m For each simulation (Simulation 1, Simulation 2 and Simulation 3), compute the following: One histogram, displaying the distribution of wheat field harvest yields on 1 December 2017 (use 10 bins); wheat) on 1 December 2017; and December 2017 .One calculation of the mean of the distribution of wheat field harvest yield (total bushels of One calculation of the standard deviation of the distribution of wheat field harvest yields on 1 (B) Assume that for all simulations, the wheat field’s mean harvest yield sells for $35 per bushel. Which of the above simulations (Simulation 1, Simulation 2 or Simulation 3) provides the greatest revenue for the mean harvest yield? (C) Now assume that chemical X costs $0.20 per bushel harvested at mean harvest yield, and that chemical Y costs $0.25 per bushel harvested at mean harvest yield. Which simulation (Simulation 1, Simulation 2 or Simulation 3) provides the greatest revenue for the mean harvest yield, under this new assumption costs for chemicals X and Y? NOTE: The total cost for each chemical is SUBTRACTED FROM THE TOTAL REVENUE produced by the mean harvest yield. Note that the mean harvest yield is given in DOLLARS PER BUSHEL, and that the costs for chemicals X and Yare given in DOLLARS PER BUSHEL Show transcribed image text
Expert Answer
Answer to Exercise 1 Population Equation Stochastic Simulation Matlab Programming Exercise 8 Pts Int Q37803464 . . .
OR