Suppose Goods X and Y Are Produced Along a Production $\frac { - X } { 2 \sqrt { 500 - X ^ { 2 } } }$

Multiple Choice

Suppose goods X and Y are produced along a production possibilities frontier 4X² + Y² = 500 and they are perfect substitutes such that U = X + Y.The slope of the production possibilities frontier is $\frac { - X } { 2 \sqrt { 500 - X ^ { 2 } } }$ .What is this slope at the utility-maximizing point?

A) 0
B) -1
C) -4
D) -5