Set 4: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Linear programming. 1. Constraints: - Weight: $50A + 40 B \leq 2000 \rightarrow 5 A + 4 B \leq 200$ - Volume: $10A + 20 B \leq 500 \rightarrow A + 2 B \leq 50$ 2. Vertices: - Intersection: $2(A + 2 B = 50) \rightarrow 2 A + 4 B = 100$. Subtract from weight eq: $(5 A+4 B) - (2 A+4 B) = 200 - 100 \rightarrow 3 A = 100 \rightarrow A = 33.3$. $B = 8.3$. - Corner 1 (Max A): $B=0, A=40$ (Weight limit). Rev: $20(40) = 800$. - Corner 2 (Max B): $A=0, B=25$ (Volume limit). Rev: $25(25) = 625$. - Intersection approx $(33.3, 8.3)$: $20(33.3) + 25(8.3) \approx 666 + 207 = 873$. - The revenue slope is between the constraint slopes. The max should be at the intersection. If $B=40$, Rev=1000. Weight: $40(40)=1600$ (OK). Vol: $20(40)=800$ (Fail).