A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≥ 90
What is the largest quantity of X that can be made without violating any of these constraints?

A) 50
B) 30
C) 20
D) 15
E) 10

To find the largest quantity of X that can be made without violating any of the constraints, we need to analyze each constraint separately and then find a common solution that satisfies all of them.1. For the first constraint, 2X + 10Y ≤ 100, if Y = 0 (to maximize X), then 2X ≤ 100, which gives X ≤ 50.2. For the second constraint, 4X + 6Y ≤ 120, if Y = 0, then 4X ≤ 120, which gives X ≤ 30.3. For the third constraint, 6X + 3Y ≥ 90, if Y = 0, then 6X ≥ 90, which gives X ≥ 15.Considering all constraints together, the largest value of X that does not violate any constraints is 30, since it is the lowest upper limit provided by the constraints.