Question

In: Math

Consider the following. optimize f(t, w) = 5t − t2 + 2w − w2 subject to...

Consider the following.

optimize f(t, w) = 5t − t² + 2w − w²

subject to g(t, w) = 2t + w = 14

(a) Write the Lagrange system of partial derivative equations. (Enter your answers as a comma-separated list of equations. Use λ to represent the Lagrange multiplier.)

(b) Locate the optimal point of the constrained system.
(t, w, f(t, w)) =

Solutions

Expert Solution

finding partial derivatives:

Writing Lagranges system of partial derivative equation:

-------------------------------

--------------------------------

Putting equatin (2) in (1):

putting this in equation g(t,w):

This point is minima.

Feel free to ask any related query in comment below, please thumbs up if you find solution helpful. Thanks.

milcah answered 1 year ago

Next > < Previous

Related Solutions

Consider the following. optimize f(r, p) = 3r2 + rp − p2 + p subject to...

Consider the following. optimize f(r, p) = 3r2 + rp − p2 + p subject to g(r, p) = 3r + 4p = 1 (a) Write the Lagrange system of partial derivative equations. (Enter your answer as a comma-separated list of equations. Use λ to represent the Lagrange multiplier.) (b) Locate the optimal point of the constrained system. (Enter an exact number as an integer, fraction, or decimal.) Once you have the answer matrix on the homescreen of your calculator,...

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t)...

1.) Use the product rule to find the derivative of (−10x6−7x9)(3ex+3) 2.) If f(t)=(t2+5t+8)(3t2+2) find f'(t) Find f'(4) 3.) Find the derivative of the function g(x)=(4x2+x−5)ex g'(x)= 4.) If f(x)=(5−x2) / (8+x2) find: f'(x)= 5.) If f(x)=(6x2+3x+4) / (√x) , . then: f'(x) = f'(1) = 6.) Find the derivative of the function g(x)=(ex) / (3+4x) g'(x)= 7.) Differentiate: y=(ln(x)) /( x6) (dy) / (dx) = 8.) Given that f(x)=x7h(x) h(−1)=2 h'(−1)=5 Calculate f'(−1) 9.) The dose-response for a specific...

Let f (t) = { 7 0 ≤ t ≤ 2π cos(5t) 2π < t ≤ ...

Let f (t) = { 7 0 ≤ t ≤ 2π cos(5t) 2π < t ≤ 4π e3(t−4π) t > 4π (a) f (t) can be written in the form g1(t) + g2(t)U(t − 2π) + g3(t)U(t − 4π) where U(t) is the Heaviside function. Enter the functions g1(t), g2(t), and g3(t), into the answer box below (in that order), separated with commas. (b) Compute the Laplace transform of f (t).

Consider the following. optimize f(x, y) = 5x2 + 4y2 − 25.1x − 11.9y + 73.9...

Consider the following. optimize f(x, y) = 5x2 + 4y2 − 25.1x − 11.9y + 73.9 subject to g(x, y) = 4x + y = 7 (b) Locate the optimal point of the constrained system. (Round all values to three decimal places.) (x, y, f(x, y)) =

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and...

Consider the following vector function. r(t) =<3t, 1/2 t2, t2> (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b). Find the curvature k(t).

. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t)...

. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t) = 5e^3t cos(4t) − 6e^2t sin(7t)

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume...

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume that each transaction is consistent. Does the final database state satisfy all integrity constraints? Explain.