Durée : environ 15 minutes
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Download the model primal1.zip. Once you have unzipped it and saved it under another name (for example primal1_approvisionnement.gms), run it using GAMS-IDE. Modify the model in order to add the constraint imposed by the government.
« A given farm can grow two types of crop : wheat and maize. The area to be cultivated must be determined for each crop, knowing that :
The objective of the farmer is to maximize his income.
Wheat yields 450€ per hectare, maize 1000€.
Wheat requires 25 hours of labour per hectare and per year, and maize 50 hours.
The farm area is 50 ha and the farmer can work 2000 hours a year.
Let us imagine that in order to ensure food supplies for cities, the government requires that every farmer cultivate at least 80 ha of cereal crops. »
Once you have run the new model, answer the questions !
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Question 1 of 4
1. Question
Download the model primal1.zip. Once you have unzipped it and saved it under another name (for example primal1_approvisionnement.gms), run it using GAMS-IDE. Modify the model in order to add the constraint imposed by the government.
« A given farm can grow two types of crop : wheat and maize. The area to be cultivated must be determined for each crop, knowing that :
The objective of the farmer is to maximize his income.
Wheat yields 450€ per hectare, maize 1000€.
Wheat requires 25 hours of labour per hectare and per year, and maize 50 hours.
The farm area is 50 ha and the farmer can work 2000 hours a year.Let us imagine that in order to ensure food supplies for cities, the government requires that every farmer cultivate at least 80 ha of cereal crops. »
Once you have run the new model, answer the questions !
What is the status of the solver ?
Correct
Incorrect
False !
The status of the solver is « Normal Completion » which means that the solver has not found an error in the writing of the model. This is shown in Solve Summary : -
Question 2 of 4
2. Question
What is the status of the model ?
Correct
Incorrect
Contrary to the status of the solver which is « Normal Completion » and which therefore indicates that there is no error in the writing of the model, the status of the model is « Infeasible ». This is shown in Solve Summary :
Indeed, one of the constraints imposes a total land area higher than 80 (government constraint) and another constraint limits the land areas to 50 (available land area constraint). Which is impossible to solve.
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Question 3 of 4
3. Question
What is the new optimum solution for wheat ?
Correct
Incorrect
As explained in the previous answer, the problem is infeasible : one constraint imposes a total land area to 80 and another limits this total to 50. Which means that there is no optimum solution, even if GAMS offers a solution ! It is therefore necessary to check the model and solver statuses.
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Question 4 of 4
4. Question
What is the new optimum solution for maize ?
Correct
Incorrect
As explained in the previous answer, the problem is infeasible : one constraint imposes a total land area to 80 and another limits this total to 50. Which means that there is no optimum solution, even if GAMS offers a solution ! It is therefore necessary to check the model and solver statuses.