If the production possibilities frontier can be expressed as $4 X ^ { 2 } + Y ^ { 2 } = 16$ then the point $X = \sqrt { 3 }$ ; $Y = 2$ is.
A)outside the production possibilities frontier
B)on the production possibilities frontier
C)inside the production possibilities frontier
D)in the wrong quadrant to be on the graph

Question

Quizplus · Accepted Answer

The production possibilities frontier is given by the equation $4X^2 + Y^2 = 16$. To check whether the point $(\sqrt{3}, 2)$ is on the production possibilities frontier, we substitute the values of $X$ and $Y$ into this equation:
$$4(\sqrt{3})^2 + 2^2 = 16$$
$$12 + 4 = 16$$
The equation is true, so the point $(\sqrt{3}, 2)$ satisfies the equation of the production possibilities frontier. Therefore, the point is on the production possibilities frontier, and the correct answer is (B).

If the Production Possibilities Frontier Can Be Expressed As 4X2+Y2=164 X ^ { 2 } + Y ^ { 2 } = 164X2+Y2=16

If the Production Possibilities Frontier Can Be Expressed As $4 X ^ { 2 } + Y ^ { 2 } = 16$