(5 pts) Given x units of capital and y units of labor, a company produces P(x, y) = 10x 1/2y 1/3 units of its product. Each unit of capital costs $2000, and each unit of labor costs $4000. Use Lagrange multipliers to find the values of x and y which maximize the company’s production if the company spends $20, 000 total on capital and labor. You may assume the maximum occurs at a point where the Lagrange multipliers condition is satisfied.

Christopher kim, cfa, is a banker with batts brothers, an investment banking firm. kim follows the energy industry and has frequent contact with industry executives. kim is contacted by the ceo of a large oil and gas corporation who wants batts brothers to underwrite a secondary offering of the company's stock. the ceo offers kim the opportunity to fly on his private jet to his ranch in texas for an exotic game hunting expedition if kim's firm can complete the underwriting within 90 days. according to cfa institute standards of conduct, kim: a) may accept the offer as long as he discloses the offer to batts brothers.b) may not accept the offer because it is considered lavish entertainment.c) must obtain written consent from batts brothers before accepting the offer.

Classify each of the following items as a public good, a private good, a natural monopoly good, or a common resource.(a) measles vaccinations (b) tuna in the pacific ocean (c) airline service in the united states (d) local storm-water system

Andy purchases only two goods, apples (a) and kumquats (k). he has an income of $125 and can buy apples at $5 per pound and kumquats at $5 per pound. his utility function is u(a, k) = 6a + 2k. what is his marginal utility for apples and his marginal utility for kumquats? andy's marginal utility for apples (mu subscript a) is mu subscript aequals 6 and his marginal utility for kumquats (mu subscript k) is