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A chemical manufacturer manufactures 2 types of chemical, A and B. Manager informs that the company has a maximum of 504 manpower hours in a week while having a minimum of 5000 litres of ingredient X. A and B contribute to 60% and 40% of the total company profit.

A would require 2,500 litres of the ingredient and 287 manpower hours in order to be produced and B would require 210 manpower hours and 2,980 litres of the ingredient in order to be produced.

Formulate the problem as a linear programming model.

My attempt,

We would want to maximize $0.6A+0.4B$ with the constraint of

$$2500A+2980B\geq5000$$ $$287A+210B\leq504$$

Is my approach correct? As I'm confused with the term 'minimum' and 'maximum'. Thanks in advance.

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    $\begingroup$ You have forgotten that $A,B\geq 0$. With it the simplex method can be applied. $\endgroup$ Apr 13, 2020 at 14:00

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for me, it seems correct. the constraints are perfectly formulated, and the profit is precise.

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  • $\begingroup$ Thanks for checking! $\endgroup$
    – Mathxx
    Apr 13, 2020 at 9:13

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