Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two Inputs of production; each unit of labor is paid the market wage (W), and each unit of capital is rented at the rental price of capital (R). Output (Y) is therefore a function of labor and capital, or Y = f(K, L), and is sold at the market price (P). The goal of this firm Is to maximize profit given the price of bots, the wage rate, the rental rate of capital, and production technology by choosing its labor and capital inputs. Fill in the following equations with the firm's profit maximization problem:
Profit = .

Alpine west, inc., operates a downhill ski area near lake tahoe, california. an all-day, adult ticket can be purchased for $55. adult customers also can purchase a season pass that entitles the pass holder to ski any day during the season, which typically runs from december 1 through april 30. the season pass is nontransferable, and the $450 price is nonrefundable. alpine expects its season pass holders to use their passes equally throughout the season. the company’s fiscal year ends on december 31. on november 6, 2009, jake lawson purchased a season ticket. required: 1. when should alpine west recognize revenue from the sale of its season passes? 2. prepare the appropriate journal entries that alpine would record on november 6 and december 31. 3. what will be included in the 2009 income statement and 2009 balance sheet related to the sale of the season pass to jake lawson?