taiwan-gsat 2025 Q16

taiwan-gsat · Other · ast__math-b 3 marks Inequalities Linear Programming (Optimize Objective over Linear Constraints)
A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions: (I) Area A does not exceed 15 hectares. (II) The sum of area A and area B does not exceed 24 hectares. (III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A. Let area A be $x$ hectares and area B be $y$ hectares.
Which of the following options for the ordered pair $(x, y)$ satisfies the above three conditions? (Single choice)
(1) $(7,15)$
(2) $(12,13)$
(3) $(14,10)$
(4) $(15,4)$
(5) $(16,8)$
A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions:\\
(I) Area A does not exceed 15 hectares.\\
(II) The sum of area A and area B does not exceed 24 hectares.\\
(III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A.\\
Let area A be $x$ hectares and area B be $y$ hectares.

Which of the following options for the ordered pair $(x, y)$ satisfies the above three conditions? (Single choice)\\
(1) $(7,15)$\\
(2) $(12,13)$\\
(3) $(14,10)$\\
(4) $(15,4)$\\
(5) $(16,8)$