Suppose X, Y, and Z are non-negative, continuous decision variables. Write a lin

Question

Suppose X, Y, and Z are non-negative, continuous decision variables. Write a linear programming constraint in terms of these variables to express the following statement (note this has already been answered by another expert so the question is complete):

a) A port can load 11 Xs per week, or 45 Ys, or 30 Zs. What combinations of X, Y, and Z can be loaded in 10 weeks?

In the first answer I received to this, the expert inferred from the given information that:

11X <= P <=12X

45Y <= P <=66Y

30Z <= P <=31Z

I don't understand how the information given implies this. Where do numbers 12, 31, and 66 come from? If the first expert's answer is incorrect, please provide a correct solution.

Explanation / Answer

It was correct that the relations are

11X <= P <= 12X

45Y <= P <= 46Y

30Z <=P <= 31Z

By combination of all these for 10 weeks we get the

(10/3)(11X + 45Y + 30Z) <= 10P <= (10/3)(12X + 46Y + 31Z)

By solving the above equation we get the equation may be

36.66X + 150Y + 100Z <= 10P <= 40X + 153.33Y + 103.33Z

Thus it is the final answer

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