# Question

Use parametric linear programming to find the optimal solution for the following problem as a function of θ, for 0 ≤ θ ≤ 20.

Maximize Z (θ) = (20 + 4θ)x1 + (30 - 3θ) x2 + 5x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

Maximize Z (θ) = (20 + 4θ)x1 + (30 - 3θ) x2 + 5x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

## Answer to relevant Questions

Simultaneously use the upper bound technique and the dual simplex method manually to solve the following problem. Minimize Z = 3x1 + 4x2 + 2x3, Subject to And 0 ≤ x1 ≤ 25, 0 ≤ x2 ≤ 5, 0 ≤ x3 ≤ 15. Consider the following problem. Maximize Z = 2x1 +5x2 +7x3, Subject to x1 + 2x2 + 3x3 = 6 and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Graph the feasible region. (b) Find the gradient of the objective function, and then find the ...Consider the Z*(θ) function shown in Fig. 8.2 for parametric linear programming with systematic changes in the bi parameters. (a) Explain why this function is piecewise linear. (b) Show that this function must be concave. Reconsider the transportation problem formulated in Prob. 9.1-7a. Without generating the Sensitivity Report, adapt the sensitivity analysis procedure presented in Secs. 7.1 and 7.2 to conduct the sensitivity analysis specified in the four parts of Prob. 9.2-22.Post your question

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