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# Algebra Bic10303

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## wan faiz

on 4 January 2013

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#### Transcript of Algebra Bic10303

PROJEK Bic10303
Muhamad Faiz safwan bin zainuddin ci120128
Pavithirah a/p gopal ai120031
Nuruljannah binti abdul razak ai120090
‘adhlin ‘atira binti mohd sopi ai120147
Linear programming is the process of taking various linear inequalities relating to some situation, and finding the “best” value obtainable under those conditions. A typical example would be taking the limitations of materials and labor, and then determining the “best” production levels for maximal profits under those conditions. The general process for solving linear-programming exercises is to graph the inequalities (called the “constraints”) to form a walled-off area on the x, y-plane (called the “feasibility region”). Introduction of linear programming A furniture manufacturer makes wooden tables and chairs. The production process involves two basic types of labor: carpentry and finishing. A table requires 2 hours of carpentry and 1 hour of finishing, and a chair requires 3 hours of carpentry and ½ of finishing. The profit is \$35 per table and \$20 per chair. The manufacturer’s employees can supply a maximum of 108 hours of carpentry work and 20 hours of finishing work per day. How many tables and chairs should be made each day to maximize profit? Study case This case about a furniture manufacturer who wants to maximize profit with \$35 per table and \$20 per chair. They have a carpentry and finishing production that tooks 2 hours for table in carpentry and 1 hour in finishing. A chair requires 3 hour of carpentry and ½ hour in finishing.

Problem Background

Table Chair Carpentry
Finishing
3 1 1/2 2 5+7= (cc) image by anemoneprojectors on Flickr Profit 35 20 ≤ 108
≤ 20
Modeling / assigning variables etc

A table requires 2 hours of carpentry and 1 hour of finishing.The manufacturers employees can supply a maximum of 108 hours of carpentry work.

2x + 3y ≤ 108

A chair requires 3 hours of carpentry and ½ of finishing.20 hours of finishing work per day.

x + 1/2y ≤ 20

The profit is \$35 per table and \$20 per chair.

Max profit = 35x + 20y

x ≥0, y ≥0
Mathematical Model
Max profit = 35x + 20y

Regular Constraints:
Constraint 1: 2x + 3y ≤ 180
Constraint 2: x + ½ ≤ 20

Non-negatively Constraints:
x ≥ 0 and y ≥ 0
Find Constraints Let x = 0
2(0) + 3y = 108
y = 36

Let y = 0
2x + 3(0) = 108
2x = 108
x = 54

Let x = 0
0 + ½y = 20
y = 20(2)
y = 40

Let y = 0
X + ½(0) = 20
x = 20 Construct The Graph
Graph Before using solver and put some mathematical formula.
Linear Programming Solution
Using Excel.
After using solver and put some formula into excel.
Sensitivity analysis.