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I am fairly new to linear programming so simplification would be helpful.
Came across a certain question and unfortunately no answer for it at the back of the book. The question is adopted from a book called An Introduction To Linear Programming And Game Theory by Paul R. Thie.
The question goes:

Premium loam is 60% soil, 40% domestic manure, and costs 5dollars per 50lb. Generic loam is 20% soil, 10% domestic manure (and 70% sand,stone,etc) and costs $1 per 50lb. We need loam for our backyard that is at least 36% soil and at least 20% domestic manure. What combination of the two loams should we use to minimize costs?

So far I have done the following:

  • Let x be the amount of premium loam bought in lb (pounds) =decision variable
  • Let y be the amount of generic loam bought in lb (pounds) =decision variable

Then some functions which if I'm not mistaken are called objective functions:
0.6x + 0.2y \ge 36
0.4x + 0.1y \ge 20
What else am I missing and how do I go about solving the problem?

Manny265
  • 159

1 Answers1

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One way to get around the the lack of a restraint on the total amount produced is:

Let $x$ be the number of pounds of premium loam used in the production of 100lbs of your final mixture. Let $y$ be the number of pounds of generic loam used in the production of 100lbs of your final mixture.

The problem is to $$\min \; \frac{5}{50}x + \frac{1}{50}y$$ subject to \begin{align} 0.6x + 0.2y &\ge 36 \\ 0.4x + 0.1y &\ge 20 \\ x+y&=100\\ x &\ge 0 \\ y &\ge 0 \\ \end{align}

MarkG
  • 532