Is it true that all of the decision variables must be positive or zero? Why?

No, it is not true that all decision variables must be positive or zero. There could be few programming equations where decision variables could ne negative. For example, customer service experience could be given a negative rating too. You want to find what is the minimum overall rating possible under given constraints. Then decision variables must be accepting negative values.
Generally decision variables are zero or positive owing to the nature of the problems solved.
 
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