Why is this question for linear programming model?

marazmatika
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I see only one variable there. Could you help me with it?

The answer involves several variables. How shall I solve it?
 

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Maybe I'm missing the point, too, but the only variable I see is how many lawyers to hire. From the data of the problem, the firm will need at least three lawyers, but not more than five. From the problem statement, I infer that they will hire all of the lawyers at one time, so there don't seem to be any complications like hiring a certain number of lawyers in a given month. Can you ask your professor to clarify this problem?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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