2. Find the solution of the following constrained maximization problems. (a) maxx.y {f(x, y) = æy...
3. Problems 2.3 Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1. That is, x +y = 1 Given this constraint, which of the following functions of x is equivalent to the original functionfx,y)=xy? f (x) = x2 f (x) = 1-r f (x) -x-x2 f(x) = x + x2 using the first order condition that f . (x) = 0, the value of x that maximizes f(x) (andfx,y)) is x- corresponding value...
Suppose that f(x,y)=xy, with the constraint that x and y are constrained to sum to 1. That is, x + y = 1. Given this constraint, which of the following functions of x is equivalent to the original function f(x,y)=xy? $$ \begin{aligned} &\tilde{f}(x)=1-x \\ &\tilde{f}(x)=x-x^{2} \\ &\tilde{f}(x)=x+x^{2} \\ &\widetilde{f}(x)=x^{2} \end{aligned} $$The langrange method can also be used to solve this constrained maximization problem.The langrangian for this constrained maximization problem is _______ Which of the following are the first order conditions for a critical...
1.Find fxy(x,y) if f(x,y)=(x^5+y^4)^6.
2. Find Cxy(x,y) if C(x,y)=6x^2-3xy-7y^2+2x-4y-3
Find (,,(Xy) if f(x,y)= (x + y) fxy(x,y) = Find Cxy(x,y) if C(x,y) = 6x² + 3xy – 7y2 + 2x - 4y - 3. Cxy(x,y)=0
6. Consider the following constrained maximization problem: 2 5 tu (х, у) x7y7 max х,у s.t Рxх + pуy < м 3, py = 4, M = 12. Answer the following questions with px a. Write down the Lagrangian function b. Derive the first order conditions c. Derive the optimality condition from those conditions d. Write the other optimality condition (since there should be two in order for us to solve for two unknowns) e. Find the optimal values for...
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)
9. Use the Lagrange Multiplier to find the relative extreme value of f(x,y) = 2x2 + 3y2 - 2xy constrained by: 2x + y = 18 {Use a table to determ F(x, y, 2) = Ans: Min: (7,4,90)
Find the constrained extrema of the function f (x, y, z) = x + y + z on the plane given by the equation x^2 + 2xy + 2y^2 + 3z^2 = 1.
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
graph please
47. x + y = -3 Find - and y-intercepts In the following exerases o g bercise find me and indoor an gran b --2-102 In the following exercises, find the intercepts for each equation 38. x - y = -4 37. x-yas 39. 3x + y = 6 40. x - 2y = 8 41. 4x - y = 8 42.5x - y = 5 43. 2x + 5y = 10 44 3x - 2y = 12...
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" – 4y' + 4y = 0; y(0) = -4, y'(0) = -1, y"(0) = -19. (b) y'' – 4y"' + 7y – by = 0; y(0) = 1, y'(0) = 0, y"(O) = 0.