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I started study Operations Research (OR) recently and I faced a problem which I struggled to modeling it to traditional OR problems. I'm not sure if such problem is a linear one nor if it can be solved using LP methods.

Problem Description I need to find the minimum purchase amount (T) to buy a batch of products, observing a restriction that each product must be purchased at least a x% of total purchase amount .

Table describing products and restrictions

Data Corn(x1) Soy(x2) Wheat(x3) Rice (x4)
Minimum Bag Weight (kg) 100 100 100 100
Unitary Price Bag ($) 4,000 3,200 4,500 1,600
Perc(% of T) of each Product 32% 27% 15% 26%

Conditions The amount of bags of each product (x1,x2,x3,x4) must be integer, i.e., no fractional bag is allowed.

The objective is to determine the minimum purchase amount to buy all of the products observing the percentage of total purchase value for each one.

If you find a solution for this, please describe which technique/method will be used and make clear what kind of OR problem is this ?

Thanks.

JRG
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  • I'm not even sure that this is on-topic here, but even if it is, what answer are you expecting? Answering the question in the title might give you 'It's XYZ Linear Programming'. Would that satisfy you, or are you looking for an actual solution? If the latter be aware that those asking homework questions are expected to have made an attempt before posting. [so] is not a free homework service. – Tangentially Perpendicular Apr 06 '22 at 03:59
  • @TangentiallyPerpendicular, first I really want to know if this problem is a Linear Programming type. If not , what kind of techniques can be used to solve it. I tried to solve it already and could not find a proper LP models that fits it, so that I'm here asking for a help. – JRG Apr 06 '22 at 05:36
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    I’m voting to close this question because it belongs on [OR.se](https://or.stackexchange.com/). – joni Apr 06 '22 at 07:06
  • @joni , you are right ! I agree to close this question in this forum. Sorry , its subject is indeed for OR group. – JRG Apr 06 '22 at 15:02

1 Answers1

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It is a linear programming problem, but it looks like there is something wrong about the question. You can't really buy, let's say 'at least 27% corn', at the moment. Percentages of each product are given with a total of 100%. So in this case they all have to be in that exact percentage or increasing one will decrease the other which is infeasible. Mathematical model for strict percentages would be:

Minimize T = 4000x1 +3200x2 +4500x3 +1600x4

4000x1 = T*(32/100)

3200x2 = T*(27/100)

4500x3 = T*(15/100)

1600x4 = T*(26/100)

x1,x2,x3,x4 >= 100

x1,x2,x3,x4 = integer
Zeynep
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