Example 1: A clock maker makes two types of wood clock to sell at various malls. It takes him 3 hours to Assemble a pine clock, which requires 2 ounces of varmish. It takes 4 hours to assemble a molave clock which takes 4 ounces of vamish. He has 8 ounces of yarmish axailable in stock and he can work 12 hours. If he makes P100 profit on each pine clock and P120 on egch.20alaxs clock, how many of each type should he make to maximize his profits? Formulate the linear program. Solution: Following the stepe in formulating a linear pogram. we have: 1. Let x = number of pine clock Y = number of roolave, clock 2. Objective function MAXIMIZE: Pxofit.P100 x +P120 y 3. Constraints Raw materials and process requirements like: Vamish requirement Processing time 4. Specific constraints Processing Vamishing 3x +4y sad2 2x + 4y Sda X20 Y2 0 Thus, the linear program would be: MAXIMIZE. Profit P100x+ P120 y SUBJECT TO: Processing Vamishing 3x + 4ys 12 2x +4y s 16 Y2 0
Example 1: A clock maker makes two types of wood clock to sell at various malls. It takes him 3 hours to Assemble a pine clock, which requires 2 ounces of varmish. It takes 4 hours to assemble a molave clock which takes 4 ounces of vamish. He has 8 ounces of yarmish axailable in stock and he can work 12 hours. If he makes P100 profit on each pine clock and P120 on egch.20alaxs clock, how many of each type should he make to maximize his profits? Formulate the linear program. Solution: Following the stepe in formulating a linear pogram. we have: 1. Let x = number of pine clock Y = number of roolave, clock 2. Objective function MAXIMIZE: Pxofit.P100 x +P120 y 3. Constraints Raw materials and process requirements like: Vamish requirement Processing time 4. Specific constraints Processing Vamishing 3x +4y sad2 2x + 4y Sda X20 Y2 0 Thus, the linear program would be: MAXIMIZE. Profit P100x+ P120 y SUBJECT TO: Processing Vamishing 3x + 4ys 12 2x +4y s 16 Y2 0
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:Example 1:
A clock maker makes two types of wood clock to sell at various malls. It takes him 3 hours to
Assemble a pine clock, which requires 2 ounces of varmish. It takes 4 hours to assemble a molave clock
which takes 4 ounces of vamish. He has 8 ounces of yarmish axailable in stock and he can work 12
hours. If he makes P100 profit on each pine clock and P120 on egch.20alaxs clock, how many of each
type should he make to maximize his profits? Formulate the linear program.
Solution:
Following the stepe in formulating a linear pogram. we have:
1. Let x = number of pine clock
Y = number of roolave, clock
2. Objective function
MAXIMIZE: Pxofit.P100 x +P120 y
3. Constraints
Raw materials and process requirements like:
Vamish requirement
Processing time
4. Specific constraints
Processing
Vamishing
3x +4y sad2
2x + 4y Sda
X20
Y2 0
Thus, the linear program would be:
MAXIMIZE. Profit P100x+ P120 y
SUBJECT TO:
Processing
Vamishing
3x + 4ys 12
2x +4y s 16
Y2 0
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