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

Cardinal company is considering a project that would require a $2,725,000 investment in equipment with a useful life of five years. at the end of five years, the project would terminate and the equipment would be sold for its salvage value of $400,000. the company’s discount rate is 14%. the project would provide net operating income each year as follows: sales $2,867,000 variable expenses 1,125,000 contribution margin 1,742,000 fixed expenses: advertising, salaries, and other fixed out-of-pocket costs $706,000 depreciation 465,000 total fixed expenses 1,171,000 net operating income $571,000 1. which item(s) in the income statement shown above will not affect cash flows? (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. any boxes left with a question mark will be automatically graded as incorrect.) (a)sales (b)variable expenses (c) advertising, salaries, and other fixed out-of-pocket costs expenses (d) depreciation expense 2. what are the project’s annual net cash inflows? 3.what is the present value of the project’s annual net cash inflows? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.) 4.what is the present value of the equipment’s salvage value at the end of five years? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.) 5.what is the project’s net present value? (use the appropriate table to determine the discount factor(s) and final answer to the nearest dollar amount.)