(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.

The monthly payment m of a loan of amount p for y years with an interest rate r can be calculated by the formula: m = p(r/12) 1 â’ (1 + r/12)â’12y calculate the monthly payment and the cummulative total payment for a $100,000 loan with an interest rate of 4.85% if taken out for 10 years, for 11 years, etc., up to a 30 year term. display the results in a three-column table where the first column is the number of years, the second is the monthly payment, and the third is the cummulative total payment. note: use format bank; for this problem. also, remember to represent the interest rate as a decimal (e.g. 0.0485) 2. a torus-shaped water tube is designed to have a volume of 8, 000in3 . the volume of the tube, v , and its surface area, s, are given by: v = 1 4 ď€ 2 (a + b)(b â’ a) 2 s = ď€ 2 (b 2 â’ a 2 ) if a = kb, determine s, a, and b for k = 0.2, 0.3, 0.7. display the results in a table

What is the main role of ctsos at the local level? at the local level, the main role of ctsos is to encourage students to become urge them to programs and competitive events.1. a.internsb.traineesc.members2.a.participateb.trainc.win

Select the correct answer a research organization conducts certain chemical tests on samples. they have data available on the standard results. some of the samples give results outside the boundary of the standard results. which data mining method follows a similar approach? o a. data cleansing ob. network intrusion o c. fraud detection od. customer classification o e. deviation detection