The Riverwood Paneling Company makes two kinds of wood paneling: Colonial and Western. The company has developed the following nonlinear programming model to determine the optimal number of sheets of Colonial paneling (x1) and Western paneling (x2) to produce to maximize profit, subject to a labor constraint: maximize Z= $25x1 - 0.8x1^2 + 30x2 - 1.2x_2^2

subject to x1 + 2x2 = 40hrs

Required:
Determine the optimal solution to this nonlinear programming model. b

True or flase? a. new technological developments can us adapt to depleting sources of natural resources. b. research and development funds from the government to private industry never pay off for the country as a whole; they only increase the profits of rich corporations. c. in order for fledgling industries in poor nations to thrive, they must receive protection from foreign trade. d. countries with few natural resources will always be poor. e. as long as real gdp (gross domestic product) grows at a slower rate than the population, per capita real gdp increases.

David paid $975,000 for two beachfront lots in coastal south carolina, with the intention of building residential homes on each. two years later, the south carolina legislature passed the beachfront management act, barring any further development of the coast, including david's lots. when david files a complaint to seek compensation for his property, south carolina refuses, pointing to a passage in david's own complaint that states "the beachfront management act [was] properly and validly designed to south carolina's " is south carolina required to compensate david under the takings clause?

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