In Exercises 7–8, use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

(4) Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra Page B: Learn1600andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…

A logistics company wants to transport wood from 3 forestry centers to 5 demand centers. Transportation costs (in euros) are shown in the following table along with production and demand at each center: F1 F2 F3 Demand D1 100 350 300 10 D2 200 300 200 20 D3 400 600 450 16 D4 350 700 300 20 D5 Production 150 500 200 7 30 20 28 What is the transportation program that minimizes the total transportation cost? Obtain an initial solution with the least cost method. Find the transportation schedule that minimizes the total transportation cost. Report the minimum total transportation cost. Indicate whether there are alternative optimal solutions, and if so, it obtains them. Please be as clear as possible. Explain all the steps of the problem. Answer all the points requested. Thank you very much.|