Question

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

Answer 1

Answer:

$X \leq 3Y$

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

$X-3Y \leq 3Y-3Y$

And we got:

$X -3Y \leq 0$

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:

$X \leq 3Y$

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

$X-3Y \leq 3Y-3Y$

And we got:

$X -3Y \leq 0$

And for this case the best answer would be:

b. X - 3Y≤ 0