Solve the following boundary value problem using finite difference method. y." = y1 Or, y:' = y2 y2' = y1 With the marginal values, y1(0) = 0, yı(1) = 9 %3D

3) The marginal price p'(x) at a supply level of x tubes per week for a certain brand of toothpaste is given by p'(x) = 0.001e0.01x Find the price-supply equation if the supplier is willing to supply 100 tubes per week at a price of $3.65 each. How many tubes would the supplier be willing to supply at a price of $3.98 each?

5. For the production of widgets the marginal revenue and marginal cost (in thousands of dollars per item) for producing x widgets are given by R'(x) = 70 – x and C'(x) = 0.1x² + 4x + 10. (a) What is the number x at which these are equal? (b) Interpret the result: for what value of x is profit maximal?