Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and of the points on the line segment S2 between points (0, -1) and (0,3). We are interested in the optimization problem min{(x − 3)² + x²y² + (y-2)² | (x, y) = S}. E Note that z* 5 since (x, y) = (2,0) is a feasible solution to this problem. 1. Determine conditions on the values of a, b, c and d for which the set E = {(x, y) = R² | a(x - c)² + b(y - d)² ≤ 1} E is convex and is such that SCE. 2. Determine the values of a and b that lead to the smallest (based on area) convex set E₁ = {(x, y) = R² | a(x)² + b(y)² ≤ 1} that is such that SCE₁. 3. Determine the values of a and b that lead to the smallest (based on area) convex set E₂ = {(x, y) = R² | a(x - 1)² + b(y - 1)² ≤ 1} that is such that S CE₂. 4. Derive a polyhedron P3 R2 that is such that S C P3 and that is the smallest possible. 5. Represent the sets S, E1, E2 and P3 graphically.

Consider the set S composed of the points on the line segment S₁ between points (-1,0) and (2,0) and of the points on the line segment S2 between points (0, -1) and (0,3). We are interested in the optimization problem min{(x − 3)² + x²y² + (y-2)² | (x, y) = S}. E Note that z* 5 since (x, y) = (2,0) is a feasible solution to this problem. 1. Determine conditions on the values of a, b, c and d for which the set E = {(x, y) = R² | a(x - c)² + b(y - d)² ≤ 1} E is convex and is such that SCE. 2. Determine the values of a and b that lead to the smallest (based on area) convex set E₁ = {(x, y) = R² | a(x)² + b(y)² ≤ 1} that is such that SCE₁. 3. Determine the values of a and b that lead to the smallest (based on area) convex set E₂ = {(x, y) = R² | a(x - 1)² + b(y - 1)² ≤ 1} that is such that S CE₂. 4. Derive a polyhedron P3 R2 that is such that S C P3 and that is the smallest possible. 5. Represent the sets S, E1, E2 and P3 graphically.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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