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« 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€. »
It is possible to develop a linear-programming model which determines the quantity of chairs and tables that must be produced in order to maximize the company turnover.
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In mathematical notation, this problem can be written as follows :
Maximize Z = 15NC + 30NT
with NC + NT ≤ 16
NC ≤ 10
NC + 4NT ≤ 40
NC ≥ 0 ; NT ≥ 0where Z company turnover (euros)
NC number of chairs
NT number of tablesTo view the corrections for each question individually, click on “view questions”
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Question 1 of 4
1. Question
« 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€. »
It is possible to develop a linear-programming model which determines the quantity of chairs and tables that must be produced in order to maximize the company turnover.
Let NC be the number of chairs sold,
NT the number of tables sold
Z the company turnoverHow can the sentence “the goal of the company is to maximize its turnover” be written in algebraic form ?
Correct
A chair is sold 15€ and a table 30€, therefore the turnover, which is the total of all sales, is the sum of the number of chairs multiplied by the price of chair and of the number of tables multiplied by the price of a table. Therefore 15NC+30NT. If Z if the company turnover to maximize therefore the mathematical formulation is as follows : Max Z = 15NC + 30NT
Incorrect
A chair is sold 15€ and a table 30€, therefore the turnover, which is the total of all sales, is the sum of the number of chairs multiplied by the price of chair and of the number of tables multiplied by the price of a table. Therefore 15NC+30NT. If Z if the company turnover to maximize therefore the mathematical formulation is as follows : Max Z = 15NC + 30NT
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Question 2 of 4
2. Question
The fabric equation says that the totality of fabric used cannot exceed the fabric available and is written as follows :
Correct
The fabric is only used for the fabrication of chairs. And each chair requires a fabric unit. Therefore the fabric used is equal to the number of chairs. This number must be less than or equal to 10, i.e. the total number of fabric units in the company.
Incorrect
The fabric is only used for the fabrication of chairs. And each chair requires a fabric unit. Therefore the fabric used is equal to the number of chairs. This number must be less than or equal to 10, i.e. the total number of fabric units in the company.
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Question 3 of 4
3. Question
The labour equation says that the labour used cannot exceed the labour available and is written as follows :
Correct
Each chair requires one hour of working time and each table requires 4 hours. The total working time is therefore the sum of the working time required for all chairs and of the working time required for all tables. Which is expressed as follows : NC + 4NT. And this time must me less than or equal to 40, i.e. the time worked by the company worker.
Incorrect
Each chair requires one hour of working time and each table requires 4 hours. The total working time is therefore the sum of the working time required for all chairs and of the working time required for all tables. Which is expressed as follows : NC + 4NT. And this time must me less than or equal to 40, i.e. the time worked by the company worker.
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Question 4 of 4
4. Question
The wood equation says that the totality of wood used cannot exceed the wood available and is written as follows :
Correct
Each table and each chair require a wood unit. Adding up the number of tables and chairs therefore leads to the number of wood units needed for their fabrication. Knowing that the company only has 16 wood units, NC+NT must be lower than or equal to 16.
Incorrect
Each table and each chair require a wood unit. Adding up the number of tables and chairs therefore leads to the number of wood units needed for their fabrication. Knowing that the company only has 16 wood units, NC+NT must be lower than or equal to 16.
