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The following file corresponds to the model developed using GAMS of the optimization of resources in a small or medium-sized company that produces tables and chairs : tablesAndChairs.zip
Download it. Once you have unzipped it, open GAMS and run the model. It corresponds to the following problem statement :
“ A company sells chairs and small tables which it produces using a stock of 16 wood units, 10 fabric units, and employs a worker for 40 hours of labour.
1 chair requires : 1 hour of labour, 1 wood unit, 1 fabric unit
1 table requires : 4 hours of labour, 1 wood unit.
A chair costs 15€, a table costs 30€. Determine the production of chairs and tables which makes it possible to maximize the company turnover.”
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Question 1 of 7
1. Question
The following file corresponds to the model developed using GAMS of the optimization of resources in a small or medium-sized company that produces tables and chairs : tablesAndChairs.zip
Download it. Once you have unzipped it, open GAMS and run the model. It corresponds to the following problem statement :“ A company sells chairs and small tables which it produces using a stock of 16 wood units, 10 fabric units, and employs a worker for 40 hours of labour.
1 chair requires : 1 hour of labour, 1 wood unit, 1 fabric unit
1 table requires : 4 hours of labour, 1 wood unit.
A chair costs 15€, a table costs 30€. Determine the production of chairs and tables which makes it possible to maximize the company turnover.”
What is the result of the goal function ?
Correct
Incorrect
False !
The objective function is written in GAMS as follows : sum(F, PRICE(F)*NU(F)) =e= Z. It is the sum of the number of pieces of furniture multiplied by the price of each piece, which is equal to Z. We asked GAMS to maximize Z while running the model, the solution is therefore found in the solve summary of the model, at the level of the « Objective Value » line :
Given that Z, apart from being the objective to maximize, is also a variable, the value of Z is also found in the variable results. We therefore must look for the “Level” of Z :
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Question 2 of 7
2. Question
How many chairs will be made ?
Correct
Incorrect
False !
The number of chairs is a variable, it is therefore found in « SolVAR ». « Lower » is the minimum value accepted by the variable, that is to say 0 here (the dot means 0), « Upper » is the maximum value, « Level » the optimum value and « Marginal » the marginal value. 8 chairs will therefore be made under optimum conditions.
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Question 3 of 7
3. Question
How many tables will be made ?
Correct
Incorrect
False !
The number of tables is a variable, it is therefore found in « SolVAR ». « Lower » is the minimum value accepted by the variable, that is to say 0 here (the dot means 0), « Upper » is the maximum value, « Level » the optimum value and « Marginal » the marginal value. 8 tables will therefore be made under optimum conditions.
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Question 4 of 7
4. Question
What is the marginal value of the wood ?
Correct
Incorrect
False !
The wood constraint is an equation. The results are therefore found in « SolEQU ». « Lower » and « Upper » are the maximum and minimum values of the equations, « Level » the optimum value and « Marginal » the marginal value.
The marginal value of wood is therefore 10 as shown in the following table.
Note that the marginal value represents the variation of the objective function if one additional unit is available, in this case wood. This means that if we had an additional wood unit (therefore 17 instead of 16) then the objective function, and therefore the company turnover, would increase by 10 euros. Which also means that the company is willing to buy a wood unit at a maximum price of 10€ (for it would earn 10€ with that same unit). -
Question 5 of 7
5. Question
What is the marginal value of labour ?
Correct
Incorrect
False !
The labour constraint is an equation. The results are therefore found in « SolEQU ». « Lower » and « Upper » are the maximum and minimum values of the equations, « Level » the optimum value and « Marginal » the marginal value.
The marginal value of labour is therefore 5 as shown in the following table.Note that the marginal value represents the variation of the objective function if one additional unit is available, in this case one hour of labour. This means that if the worker worked one more hour (therefore 41 instead of 40) then the objective function, and therefore the company turnover, would increase by 5 euros. Which also means that the company is willing to pay one additional hour of labour at a maximum price of 5€ (for it would earn 5€ with that same unit).
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Question 6 of 7
6. Question
What is the maximum which the fabric value can reach ?
Correct
Incorrect
False !
The fabric constraint is an equation. The results are therefore found in « SolEQU ». « Lower » and « Upper » are the maximum and minimum values of the equations, « Level » the optimum value and « Marginal » the marginal value.
The marginal value of fabric is therefore 5 as shown in the following table. -
Question 7 of 7
7. Question
What is the optimum value reached by the labour variable ?
Correct
Incorrect
False !
The fabric constraint is an equation. The results are therefore found in « SolEQU ». « Lower » and « Upper » are the maximum and minimum values of the equations, « Level » the optimum value and « Marginal » the marginal value. The optimum value can therefore be found in the “Level” column, the quantity of labour is 40 (hours).
