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A linear programming problem contains a restriction that reads "the quantity of X must be at most three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

a. 3X ≥ Y
b. X - 3Y≤ 0
c. X + Y≥3
d. X - 3Y ≥ 0
e. 3X ≤ Y

Respuesta :

Answer:

[tex] X \leq 3Y[/tex]

And we can rewrite this expression like this, subtracting 3Y from both sides of the last inequality:

[tex] X-3Y \leq 3Y-3Y[/tex]

And we got:

[tex] X -3Y \leq 0 [/tex]

And for this case the best answer would be:

b. X - 3Y≤ 0

Explanation:

For this case we need the following condition: "the quantity of X must be at most three times as large as the quantity of Y."

And we can convert this into a mathematical formula like this:

[tex] X \leq 3Y[/tex]

And we can rewrite this expression like this, subtracting 3Y from both sides of the last inequality:

[tex] X-3Y \leq 3Y-3Y[/tex]

And we got:

[tex] X -3Y \leq 0 [/tex]

And for this case the best answer would be:

b. X - 3Y≤ 0

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