A firm that using a single variable input to produce output in the short run faces increasing marginal product with respect to that input. Which of the following statements are correct? (Select all that apply)

a.There is a finite allocation of input that satisfies the first and second order profit maximizing conditions

b.The firm should produce zero in the short-run profit maximizing solution.

c.The first order condition to the profit maximization problem will identify a profit minimizing allocation of inputs

d.The firm will want to produce an arbitrarily large amount of output in the profit maximizing solution.