A firm operating in a perfectly competitive market has the option to use two different technologies to produce a good. The first technology exhibits constant returns to scale, where the output (Y) is equal to the product of a productivity measure (A) and the allocated flow of machine-hours (K). The second technology demonstrates decreasing returns to scale, and the output (Y) is the square root of the allocated flow of machine-hours (K). The firm has a total flow of machine-hours (K) available. The objective is to maximize the sum of Y and Y, while adhering to the resource constraint that the sum of K and K must equal K. (Consider that both A,K > 0)