A hat manufacturing firm has the following production function with capital and labor being the inputs: Q = min(5L,3K) (it has a fixed-proportions production function). a) If w is the cost of a unit of labor and r is the cost of a unit of capital, derive the firm’s optimal inputs, long-run total cost curve, average cost curve, and marginal cost curve in terms of the input prices and Q.
b) A firm has the linear production function Q = 2L + 7K. Derive the expression for the optimal inputs and the 1ong-run total cost that the firm incurs, as a function of Q and the factor prices, w and r

He cheyenne hotel in big sky, montana, has accumulated records of the total electrical costs of the hotel and the number of occupancy-days over the last year. an occupancy-day represents a room rented out for one day. the hotel's business is highly seasonal, with peaks occurring during the ski season and in the summer. month occupancy- days electrical costs january 1,736 $ 4,127 february 1,904 $ 4,207 march 2,356 $ 5,083 april 960 $ 2,857 may 360 $ 1,871 june 744 $ 2,696 july 2,108 $ 4,670 august 2,406 $ 5,148 september 840 $ 2,691 october 124 $ 1,588 november 720 $ 2,454 december 1,364 $ 3,529 required: 1. using the high-low method, estimate the fixed cost of electricity per month and the variable cost of electricity per occupancy-day. (do not round your intermediate calculations. round your variable cost answer to 2 decimal places and fixed cost element answer to nearest whole dollar amount) 2. what other factors other than occupancy-days are likely to affect the variation in electrical costs from month to month? (you may select more than one answer. single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer.) seasonal factors like winter or summer. systematic factors like guests, switching off fans and lights. number of days present in a month. fixed salary paid to hotel receptionist. income taxes paid on hotel income.