Goal Programming (Lindo)
Not what you're looking for?
First West Chemical
First West Chemical Company produces two chemical ingredients for pharmaceutical firms; formula X and formula Y.
Production of each ingredient requires two processes.
A unit of Formula X requires 4 hours in process 1 and 3 hours in process 2.
A unit in formula Y requires 2 hours in process 1 and 5 hours in process 2.
The normal operating production times for the two processes are as follows: process 1, 70 hours and process 2, 60 hours.
The production process of formula X results in one unit of a by-product called XZ. Four (4) units of X produce 1 unit of XZ.
The production process for formula Y yields 5 units of a by-product, YK for each unit of formula Y.
The unit profits for formulas X and Yare $10,000 and $15,000 respectively.
By products XZ yields $6000 unit profit.
By product YK yields a $3000 unit profit for up to 15 units.
Because of the limited market and the danger involved in handling the material, any by product YK in excess of 15 units must be destroyed at a unit cost of $4,000.
Also due to storage regulations, no more than 15 units of Formula X can be produced.
The management at this chemical company has established the following goals in order of importance:
1. Avoid any underutilization of normal operation hours of each of the two processes. Each of equal importance.
2. Meet the outstanding orders for 8 units of formula X and 7 units of Formula Y. Each of equal importance.
3. Limit any overtime operation of each of the two production process to 10 hours. Each of equal importance.
4. Achieve a profit goal of $220,000
5. Limit the production of by-product YK to 15 units.
6. Minimize the overtime operation of the production processes. Each of equal importance.
Formulate this problem into a mathematical model and using LINDO determine the solution that best satisfies these goals.
this is what I have so far.....
GOAL #1: Avoid any underutilization of normal operation hours of each of the two processes. Each of equal importance.
Process #1
4FX + 2FY + S1M - S1P = 70
where
FX = # of units of formulea X
FY = # of units of formulea Y
S1M = UNDERutilization of process 1 at 70 hours
S1P = OVERutilizaztion of process 1 at 70 hours
Process #2
3FX + 5FY + S2M - S2P = 60
where
FX = # of units of formulea X
FY = # of units of formulea Y
S2M = UNDERutilization of process 2 at 60 hours
S2P = OVERutilizaztion of process 2 at 60 hours
GOAL 1 CONSTRAINT
4FX + 2FY + S1M - S1P = 70
3FX + 5FY + S2M - S2P = 60
GOAL 1 OBJECTIVE FUNCTION
MIN Z = S1M + S2M
GOAL #2: Meet the outstanding orders for 8 units of formula X and 7 units of Formula Y. Each of equal importance.
GOAL 2 CONSTRAINT
FX + S3M - S3P = 8
FY + S4M - S4P = 7
GOAL 2 OBJECTIVE FUNCTION
MIN S3M + S4M
GOAL 3. Limit any overtime operation of each of the two production process to 10 hours. Each of equal importance.
The normal operating production times for the two processes are as follows: process 1, 70 hours and process 2, 60 hours.
Anything greather than 70hrs or 60hrs is considered OT.
GOAL 3 CONSTRAINT
S1P + S12M - S12P = 10
S2P + S22M - S22P = 10
GOAL 3 OBJECTIVE FUNCTION
MIN S12P + S22P
where
S12M = negative deviation of OT from 10 hours in process 1
S12P = OT beyond 10 hours in process 1
S22M = negative deviation of OT from 10 hours in process 2
S22P = OT beyond 10 hours in process 2
GOAL 4. Achieve a profit goal of $220,000
10000FX + 15000FY + 6000XZ + 3000YK - YM4000 - YN4000 = 220000
YM + YN = 1
YM = LESS THAN 15 UNITS OF XXXXXXX
YN = GREATER THAN 15 UNITS OF XXXXXX
GIN YM
GIN YN
GOAL 5. Limit the production of by-product YK to 15 units.
15 UNITS OF YK = 5 * 15 = 75 UNITS OF FY
THEREFORE,
FY <= 75
GOAL 6. Minimize the overtime operation of the production processes. Each of equal importance.
MIN S12P + S22P
Purchase this Solution
Solution Summary
Word file contains clear instructions with formulations and solutions for all the goals.
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.