Solved: Investigation Consider the objective function subject to the constraint Assume

Chapter 13, Problem 80

(choose chapter or problem)

Investigation Consider the objective function f(x, y) = ax + by subject to the constraint \(x^{2} / 64+y^{2} / 36=1\). Assume that x and y are positive.

(a) Use a computer algebra system to graph the constraint. For a = 4 and b = 3, use the computer algebra system to graph the level curves of the objective function. By trial and error, find the level curve that appears to be tangent to the ellipse. Use the result to approximate the maximum of f subject to the constraint.

(b) Repeat part (a) for a = 4 and b = 9.

Text Transcription:

x^2 / 64 + y^2 / 36 = 1

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