Digital SATMath: AlgebraMedium
A company produces two types of widgets, A and B. Widget A requires 2 hours of assembly and 1 hour of finishing. Widget B requires 3 hours of assembly and 1 hour of finishing. There are a maximum of 120 assembly hours and 50 finishing hours available per day. Let 'a' be the number of Widget A produced and 'b' be the number of Widget B produced. Which system of inequalities represents the constraints on production?
- A2a + 3b ≤ 120 a + b ≤ 50
- B2a + b ≤ 120 3a + b ≤ 50
- C3a + 2b ≤ 120 a + b ≤ 50
- Da + b ≤ 120 2a + 3b ≤ 50
Show answer & explanationAnswer & explanation
Correct answer: A. 2a + 3b ≤ 120 a + b ≤ 50
For assembly hours: Widget A takes 2 hours (2a) and Widget B takes 3 hours (3b). The total assembly hours cannot exceed 120, so 2a + 3b ≤ 120. For finishing hours: Widget A takes 1 hour (a) and Widget B takes 1 hour (b). The total finishing hours cannot exceed 50, so a + b ≤ 50.
Why the other options are wrong
- B. The assembly constraint is incorrect (2a + b ≤ 120) and the finishing constraint is incorrect (3a + b ≤ 50).
- C. The assembly constraint is incorrect (3a + 2b ≤ 120). The finishing constraint is correct but the assembly one is not.
- D. Both constraints are incorrectly formulated regarding the coefficients and maximums.
Systems of Linear Inequalities
A set of two or more linear inequalities involving the same variables. The solution to a system of linear inequalities is the region where the solutions of all inequalities overlap.
- Used to model real-world constraints or boundaries.
- Each inequality represents a boundary line and a shaded region.
- The solution set is typically a feasible region in a graph.
Memory trick: Constraints are like fences: know what's allowed and what's restricted.