The solution given in the solution manual of the book is:

But since the processes are sequential and not concurrent, I believe the inequality should be: $(10+6+8)x_1 + (5+20+10)x2 \le 600$
Can anyone explain why this is wrong?
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The inequality constraint is not correct, since it has a limit of only up to $600$ production minutes per day; the $600$ minutes are allocated for all the three processes.
In the given solution there are not only $600$ productive minutes, but three times that time, because the processes are sequential. There is a constraint separately for each process, each of them are allocated 10 hours.