ITPEC FE Morning October 2021 Question 79

The company wants to minimize total ad cost while meeting exposure requirements. Let x = number of TV ads, y = number of Radio ads.

Building the constraints from the table (read by column, not by row):

• •In the city column: TV gives 8 points, Radio gives 10 points. Requirement is at least 60 → 8x + 10y ≥ 60
• •Outside the city column: TV gives 6 points, Radio gives 3 points. Requirement is at most 40 → 6x + 3y ≤ 40
• •Non-negativity: x ≥ 0, y ≥ 0

Objective function: minimize cost → 2000x + 800y → minimize

This matches (d).

Why not others:
- (a) Uses ≤ 60 for in-city (wrong direction — we need at least 60) and wrong coefficients (mixes columns)
- (b) Has ≥ 60 (correct direction) but wrong coefficient pairing — 8x + 6y mixes TV's in-city (8) with TV's outside-city (6) in the same constraint instead of reading down one column
- (c) Uses ≤ 60 for in-city (wrong direction — should be ≥) and also has swapped coefficients

Key rule: In LP table problems, each constraint is built from one column (one requirement type), not one row. "At least" → ≥, "at most" → ≤. Always verify which variable maps to which row before writing coefficients.

AI-generated — may contain errors