A firm has the production function: =(,)=2. Let , , and denote the price of output, the wage rate, and the rental rate, respectively.(1) Show that the firm's production satisfies diminishing marginal rate of technical substitution and constant returns to scale.(2) Suppose v is equal to $100 per unit, w is equal to $20per unit, and capital is fixed at =5. Find the firm's short-run total cost function, short-run average variable cost functionand short-run marginal cost function.(3) Based on the information in part (2),find the firm's short-run supply curve.