Find the optimal solution for all values

Assignment Help Mathematics

Reference no: EM13714124

Deterministic models / linear programming. Please help asap

1. Consider the following parametric problem:

z(θ) = min - 10x1 + 16x2 - x3

x1 - 2x2 + x3 ≤ 2 + 2θ

x1 - x2 ≤ 4 + θ

x1, x2, x3 ≥ 0,

where θ is a parameter.

(a) Solve the LP for θ = 0 and compute the optimal shadow prices.

(b) For what values of θ does the basis computed in part a) remain optimal?

2. Consider the following optimization problem:

z(θ) = max (-3 + 3θ)x1 + (1 - 2θ)x2

- 2x1 + x2 ≤ 2

x1 - 2x2 ≤ 2x1 - x2 ≤ 4

x1, x2 ≥ 0.

(a) Use the parametric programming algorithm to find the optimal solution for all values of θ. Are there values of θ such that the objective is unbounded?

(b) Plot the optimal objective value as a function of θ.

(c) Graph the feasible region for the above problem (in terms of x1 and x2) and interpret the parametric algorithm on the graph.

Reference no: EM13714124

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