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Excel Solver HELP Linear Programming (product mix)

Would somebody be able to check whether this problem is correct?

if i change the 'make unconstrainted variables non-negative' so it isnt ticked i get a different answer

also if in an transportation problem if the demand (10000) is higher than the supply (9000) are the demand constraints the correct way?

SUPPLY
X11 + X12 + X13 ≥5000
X21 + X22 + X23 ≥4000

DEMAND
X11 + X21 ≥ 3000
X12 + X22 ≥ 4000
X13 + X23 ≥ 3000

thanks

(edited 7 years ago)

LinearProgrammingTables.xlsx10.6KB

Reply 1

ghostwalker

Original post by JoeyA95

Would somebody be able to check whether this problem is correct?

if i change the 'make unconstrainted variables non-negative' so it isnt ticked i get a different answer

I'm using an older version (2007) of Excel, so may not be of any use, and see no change: x1=30, x2=0 in both cases.
Edit: I'm aware that later versions have changed the wording of that Excel option (it's different in my earlier version), and potentially changed what's behind the scenes.

(edited 7 years ago)

Reply 2

JoeyA95

Original post by ghostwalker

I'm using an older version (2007) of Excel, so may not be of any use, and see no change: x1=30, x2=0 in both cases.
Edit: I'm aware that later versions have changed the wording of that Excel option (it's different in my earlier version), and potentially changed what's behind the scenes.

ok im guessing that x1=30 x2=0 is the correct answer then?

Reply 3

ghostwalker

Original post by JoeyA95

ok im guessing that x1=30 x2=0 is the correct answer then?

What other solution do you get?

Reply 4

JoeyA95

Original post by ghostwalker

What other solution do you get?

x1=20 x2=20

Reply 5

ghostwalker

Original post by JoeyA95

x1=20 x2=20

Both solutions give the same cost.

And so will any linear combination of the form

\lambda(30,0) + (1-\lambda)(20,20)

where

\lambda \in [0,1]

, subject to the values being integers.

The Excel parameter is a red herring - just results in different methods behind the scenes, hence the two extreme ends of the viable solutions.

(edited 7 years ago)

Reply 6

JoeyA95

Original post by ghostwalker

What other solution do you get?

for the transporation problem are the constraints the correct way?

Reply 7

JoeyA95

Original post by ghostwalker

Both solutions give the same cost.

And so will any linear combination of the form

\lambda(30,0) + (1-\lambda)(20,20)

where

\lambda \in [0,1]

, subject to the values being integers.

The Excel parameter is a red herring - just results in different methods behind the scenes, hence the two extreme ends of the viable solutions.

ok i will use the x1=30 x2=0 as you got this aswell

Reply 8

ghostwalker

Original post by JoeyA95

for the transporation problem are the constraints the correct way?

They are correct for the demand.

But should be the other way around for the supply.

Note: With that there is no feasible solution. You need to add a dummy source to make up the missing supply.