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I'm not understanding how there can be two separate solutions to this problem. I've doubled checked and followed all the steps but I'm assuming my answer is wrong but similar?

Sorry, I don't have the reputation to embed:

Here is the original question, write the Dual of this System:

Here is the original question, write the Dual of this System

Here is the solution to this problem:

Here is the solution to this problem

Here is my Solution: Here is my Solution

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Let $y_1 = -p_1$, $p_2=y_2, p_3=y_3$ and $y_4$ as the surplus variable and your formulation are equivalent.

By viewing $x_1 \le 0$ as a signed constraint rather than a regular constraint, you can actually save a variable, i.e. the formulation given in the book.

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