A furniture company produces school tables and chairs. The production of each product requires a certain number of hours of carpentry work and a certain number of labour hours of painting work. Each table takes 4 hours of carpentry and 2 hours of painting; and each chair requires 3 hours of carpentry and 1 hour of painting. At the beginning of June 2022, the company had a stock of 45 tables and 60 chairs. By the end of June, the company needs to meet an order of 60 tables and 90 chairs from a local school. Under the condition that this order has to be met on time, the company's goal is to maximise the combined sum of the numbers of tables and chairs after the order is delivered. Under the current working condition, the company can allocate 240 hours of carpen- try work and 100 hours of painting work. (1) Formulate the constraint maximisation task as a linear programming problem. You need to specify the target function to be maximised, and all constraints to be imposed. (2) Present a hand-drawing graph to illustrate this maximisation problem. A ruler needs to be used when drawing straight lines, and the coordinates on the vertical axis and horizontal axis need to be marked. Note that you can take a photo of your graph and submit it together with your answer sheet. (3) Find out all possible points, which are most likely to be the maximum point (that is, the point which maximises the target function). (4) Of all the points identified in (3), decide which point is the solution to this maximisa- tion problem.
A furniture company produces school tables and chairs. The production of each product requires a certain number of hours of carpentry work and a certain number of labour hours of painting work. Each table takes 4 hours of carpentry and 2 hours of painting; and each chair requires 3 hours of carpentry and 1 hour of painting. At the beginning of June 2022, the company had a stock of 45 tables and 60 chairs. By the end of June, the company needs to meet an order of 60 tables and 90 chairs from a local school. Under the condition that this order has to be met on time, the company's goal is to maximise the combined sum of the numbers of tables and chairs after the order is delivered. Under the current working condition, the company can allocate 240 hours of carpen- try work and 100 hours of painting work. (1) Formulate the constraint maximisation task as a linear programming problem. You need to specify the target function to be maximised, and all constraints to be imposed. (2) Present a hand-drawing graph to illustrate this maximisation problem. A ruler needs to be used when drawing straight lines, and the coordinates on the vertical axis and horizontal axis need to be marked. Note that you can take a photo of your graph and submit it together with your answer sheet. (3) Find out all possible points, which are most likely to be the maximum point (that is, the point which maximises the target function). (4) Of all the points identified in (3), decide which point is the solution to this maximisa- tion problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A furniture company produces school tables and chairs. The production of each product
requires a certain number of hours of carpentry work and a certain number of labour
hours of painting work. Each table takes 4 hours of carpentry and 2 hours of painting;
and each chair requires 3 hours of carpentry and 1 hour of painting.
At the beginning of June 2022, the company had a stock of 45 tables and 60 chairs. By
the end of June, the company needs to meet an order of 60 tables and 90 chairs from a
local school. Under the condition that this order has to be met on time, the company's
goal is to maximise the combined sum of the numbers of tables and chairs after the order
is delivered.
Under the current working condition, the company can allocate 240 hours of carpen-
try work and 100 hours of painting work.
(1) Formulate the constraint maximisation task as a linear programming problem. You
need to specify the target function to be maximised, and all constraints to be imposed.
(2) Present a hand-drawing graph to illustrate this maximisation problem. A ruler needs
to be used when drawing straight lines, and the coordinates on the vertical axis and
horizontal axis need to be marked. Note that you can take a photo of your graph and
submit it together with your answer sheet.
(3) Find out all possible points, which are most likely to be the maximum point (that is,
the point which maximises the target function).
(4) Of all the points identified in (3), decide which point is the solution to this maximisa-
tion problem.
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