maximize q = xy, where x and y are positive numbers such that x + 25/3 y^2 = 16. write the objective…

maximize q = xy, where x and y are positive numbers such that x + 25/3 y^2 = 16. write the objective function in terms of y. q = □ (type an expression using y as the variable.)

maximize q = xy, where x and y are positive numbers such that x + 25/3 y^2 = 16. write the objective function in terms of y. q = □ (type an expression using y as the variable.)

Answer

Explanation:

Step1: Isolate x from the constraint

Given $x+\frac{25}{3}y^{2}=16$, we can solve for $x$ as $x = 16-\frac{25}{3}y^{2}$.

Step2: Substitute x into the objective function

The objective function is $Q=xy$. Substituting $x = 16-\frac{25}{3}y^{2}$ into it, we get $Q=(16 - \frac{25}{3}y^{2})y=16y-\frac{25}{3}y^{3}$.

Answer:

$16y-\frac{25}{3}y^{3}$