Asked by christian
A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?
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GPT-5 mini
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Let x = number of sofas and y = number of pillow pairs. Each pair is 2 pillows, so the total number of items is x + 2y. The wholesaler requires at least 4 items, so
x + 2y ≥ 4.
The boundary line is x + 2y = 4 (or y = 2 − x/2), which has intercepts (0,2) and (4,0) and slope −1/2. The feasible region is the half-plane on the side of that line away from the origin (the region satisfying x + 2y ≥ 4), further restricted in the real scenario to x ≥ 0, y ≥ 0 and y an integer (pairs).
x + 2y ≥ 4.
The boundary line is x + 2y = 4 (or y = 2 − x/2), which has intercepts (0,2) and (4,0) and slope −1/2. The feasible region is the half-plane on the side of that line away from the origin (the region satisfying x + 2y ≥ 4), further restricted in the real scenario to x ≥ 0, y ≥ 0 and y an integer (pairs).
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