Consider the following linearly constrained optimization problem: max f(x) = 32.r1 + 50x2 10 +...

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Consider the following linearly constrained optimization problem: max f(x) = 32.r1 + 50x2 – 10 + r- 2 - a s.t. 3x1 + x2 < 11 2x1 + 5x2 < 16 21, 22 >0 (a) Prove that this is a convex programming problem. (b) Ignore the constraints and let #1 = #2, use the bisection method with e = 0.01 and initial bounds 1.5 and 2.5 to solve the problem. Consider the following linearly constrained optimization problem: max f(x) = 32.r1 + 50x2 – 10 + r- 2 - a s.t. 3x1 + x2 < 11 2x1 + 5x2 < 16 21, 22 >0 (a) Prove that this is a convex programming problem. (b) Ignore the constraints and let #1 = #2, use the bisection method with e = 0.01 and initial bounds 1.5 and 2.5 to solve the problem.