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A gardener needs AT LEAST 10 units of chemical A. A jar gives 5 units and a carton 1 unit. The constraint is:
A$5x+y\le 10$
B$5x+y=10$
C$x+5y\ge 10$
D$5x+y\ge 10$
Answer & Solution
Correct answer: D. $5x+y\ge 10$
1. The phrase 'at least' sets a floor, not a ceiling, so the inequality points the greater-than way.
2. Each jar supplies 5 units of chemical A, so $x$ jars supply $5x$.
3. Each carton supplies 1 unit, so $y$ cartons supply $y$.
4. The total must reach the requirement: $5x+y\ge 10$.
5. Writing $\le$ instead of $\ge$ was the single most common recorded error, and it would let the gardener buy nothing at all.
_Source: NECTA ACSEE 2022 Advanced Mathematics 142/1, Question 3: Linear Programming_
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