Final answer:
To write the objective function in terms of y, we need to eliminate x from the equation x - 16/3y² = 1. We can do this by rearranging the equation to express x in terms of y and then plugging this value into the objective function qxy.
Step-by-step explanation:
We want to maximize the expression qxy, where x and y are positive numbers and x - \frac{16}{3y^2} = 1. To write the objective function in terms of y, we need to eliminate x from the equation. Rearranging the equation, we have x = 1 + \frac{16}{3y^2}. Plugging this value of x into the objective function, we get q(1 + \frac{16}{3y^2})y. Simplifying further, we have qy + \frac{16q}{3y}.