Question

Maximize Q = xy, where x and y are positive numbers such that (x + 3y² = 1). Write the objective function in terms of y.

A) (y(1-3y²))
B) (y(1+3y²))
C) (y(1-9y²))
D) (y(1+9y²))

Answer 1

To maximize Q = xy, we can express the objective function in terms of y as (y - 3y³). The correct answer is option A) (y(1-3y²)).

Step-by-step explanation:

To maximize Q = xy, we need to express the objective function in terms of y. Given the equation x + 3y² = 1, we can rearrange it to solve for x, which gives us x = 1 - 3y². Substituting this expression for x, we get Q = (1 - 3y²)y = y - 3y³.

The objective function in terms of y is therefore (y - 3y³). Option A) (y(1-3y²)) matches this expression, so the correct answer is A).