question archive A furniture company is producing tables and chairs for the coming week
A furniture company is producing tables and chairs for the coming week
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A furniture company is producing tables and chairs for the coming week. The production of tables and chairs will go through two processes: wood cutting and assembly. In the wood cutting process, the required labor hour is 1 hour for a chair and 2 hours for a table. In the assembly process, the required labor hour is 4 hours for a chair and 3 hours for a table. For the coming week, the maximum assembly hours for the wood cutting process and 180 hours for the decides process. Based on the company's inventory level, the company to produce no more than 100 chairs and 30 tables for the coming week. Suppose the profit margin is $5/chair and $6/table. Set up a programming model to maximize the total profit for this furniture company and solve the model using Excel Solver.
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Answer:
The data given is summarized as follows:
|
Products |
Chairs |
Tables |
|
|
Unit Profit margin |
$5 |
$6 |
|
|
Resources |
Resource required per unit |
Resource available |
|
|
Wood cutting process labor hours |
1 |
2 |
70 |
|
Assembly labor hours |
4 |
3 |
180 |
Decision Variable:
Let,
X = units of chairs to be produced
Y = units of tables to be produced
Objective function:
The company’s objective is maximizing total profit margin of production mix. The profit function is given as follows:
Max Z = $5X + $6Y
Subjected to:
The objective function is subjected to following constraints:
Wood-cutting process labor-hours constraint: Maximum labor hours available are 70 hours.
X + 2Y <= 70
Assembly labor hours constraint: Maximum labor hours available are 180 hours.
4X + 3Y <= 180
Maximum production limit for chairs is 100 units:
X <= 100
Maximum production limit for tables is 30 units:
X <= 30
Non-negative constraint: The production quantities required cannot be negative.
X, Y >= 0
The spreadsheet model:
Optimal Solution:
Units of Chairs = 70 units
Units of Tables = 0 unit
Optimal Profit = $350
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