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Hi,
I handed in my solution and it came back to me because I forgot to complete a part.
They want me to calculate the ranges for the objective co-efficients and I just can't see anywhere that explains how to do that....
I found the optimum point and the shadow prices, but what is actually meant by "the ranges for the objective co-efficients" ?
Thanks, Martha
Hi Bob,
Again thank you for the clear explanation.
I added the x, y and z to the sales and converted them to decimals as you suggested and I was left with
Max P = 0.1x + 0.1y + 0.035z
If I multiply that line by 1000 I get Max P = 100x + 100y + 35z
Just wondering if I multiply the profit line by 1000, do I also have to multiply the constraints by 1000 ?
I'm guessing not because 50000 x 1000 = 50000000 which seems like a very big number to be dealing with.
Thanks for the tip about that site, it's very helpful
Thanks, Martha
Hi Bob,
Thank you for the reply and I think I'm starting to see this a little clearer.
I'm down as far as getting the constraints and I think that's fine as I have
0.40x + 0.20y <= 50000
0.40x + 0.50y + 0.65z <= 75000
0.20x + 0.30y + 0.35z <= 80000
After that is maybe where I'm going wrong. I've calculated the cost as
$ x/1000 times 200 = $ x/5
$ y/1000 times 100 = $ y/10
$ z/1000 times 65 = $ 13z/200
I've calculated the sales as
For x you’ll sell at $ 30/100
For y you’ll sell at $ 20/100
For z you’ll sell at $ 10/100
Now you say the profit expression is sales minus the cost. When I do that I get
Max P = (30/100 – x/5) + (20/100 – y/10) + (10/100 – 13z/200)
This is where I think I might be gone wrong because the examples in my book seem to have a "neater" looking profit expression, usually something like Max P = 40x + 50y +30z
Thanks, Martha
Hi,
I'm having a problem with the following word problem. The whole thing about the quantities of material available is throwing me because the numbers are huge.
A pig feed company produce three different qualities of pig feed. In each product there are a blend of three raw materials.
Feed 1 sells at $30 per 100kg bag and is made of 40% of material A, 40% of material B and 20% of material C.
Feed 2 sells at $20 per 100kg bag and is made of 20% of material A, 50% of material B and 30% of material C.
Feed 3 sells at $10 per 100kg bag and is made of 65% of material B and 35% of material C.
Material A costs $200 per 1000kg and there are 50,000kg available.
Material B costs $100 per 1000kg and there are 75,000kg available.
Material C costs $65 per 1000kg and there are 80,000kg available.
Re-write this as a as a linear programming problem showing the Max and constraints ? ?
What I have so far is this and I’m not sure if I now multiply the $200 by 50, and so on…. ? ?
Material A Material B Material C Price per 100kg
Feed 1 40 40 20 30
Feed 2 20 50 30 20
Feed 3 65 35 10
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