A linear programming problem has three constraints, plus nonnegativity constraints on X and Y. The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 100; 6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

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The largest quantity of X that can be made without violating any of these constraints can be found by testing the limits set by each constraint. The third constraint, 6X + 3Y ≥ 90, can be rearranged to find the minimum X when Y is 0 (to maximize X), resulting in X ≥ 15. However, to find the maximum X, we need to consider all constraints together. The first constraint, 2X + 10Y ≤ 100, when Y is 0, allows for X to be up to 50. The second constraint, 4X + 6Y ≤ 100, also allows for X to be up to 25 when Y is 0. Considering all constraints together, the maximum X that does not violate any constraints, especially focusing on the most restrictive one (the second constraint), is 25.

A Linear Programming Problem Has Three Constraints, Plus Nonnegativity Constraints