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fiona1110

Guest

Linear programming question

The Department of Mathematics and Statistics, ABC has been awarded a funding to develop a new mathematical model to solve the timetabling problem. The department estimates that 500 hours will be required to complete the project. However, only four members are available for the research and they are Benson (faculty member), William (faculty member), Marco (faculty member) and Jo Jo (research assistant). Because Benson and William are the supervisors of the project, they must be assigned at least 70% of the total number of hours. To provide research experience for Jo Jo, Jo Jo must be assigned at least 15% of the total project time. However, due to other departmental duties and responsibilities, Marco has a maximum of 30 hours available to work on this project. Hourly wage rates are $50 for Benson, $45 for William, $45 for Marco and $20 for Jo Jo.

Denote
B = number of hours assigned to Benson
W = number of hours assigned to William
M = number of hours assigned to Marco
E = number of hours assigned to Jo Jo

a) Formulate a linear program that can be used to determine the number of hours each member should be assigned to the project in order to minimize total cost.

b) How many hours should each member be assigned to the project? What is the total cost?

c) ABC now wants to adjust the hourly wages of each of the members and the total number of working hours. Generate a sensitivity report with the aid of Microsoft Excel.

d) If ABC raises the salaries of Benson and Jo Jo by 10%, are the total working hours (found in b.) still the optimal for the project? Explain.

e) Suppose the maximum number of hours assigned to Marco could be more than 30 hours. What effect would this have on the optimal solution? Explain.

f) If Jo Jo were not required to work a minimum number of hours on this project, would the optimal solution change? Explain

i'm stuck on part b
Plz help me, thank you

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Linear programming question

hi fiona1110,

Welcome to the forum. 

i'm stuck on part b

So what have you got for part a?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

fiona1110

Member

Registered: 2014-10-15

Posts: 2

Re: Linear programming question

hi Bob,

Min 50B+45W+45M+20E
St. B+W+M+E=500
B+W=>350
E=>75
M<=30
B,W,M,E=>0

is it correct?

Fiona

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Linear programming question

hi Fiona,

Yes, those look good to me.  So give me a moment to get an solution. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Linear programming question

Sorry, that took a while.  I had to find a four variable solver on-line.  I eventually found

http://www.zweigmedia.com/RealWorld/simplex.html

which gave b = 0, w = 350, m = 0 and e = 150.

How does that seem?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob