# Question: This chapter has described the simplex method as applied to

This chapter has described the simplex method as applied to linear programming problems where the objective function is to be maximized. Section 4.6 then described how to convert a minimization problem to an equivalent maximization problem for applying the simplex method. Another option with minimization problems is to make a few modifications in the instructions for the simplex method given in the chapter in order to apply the algorithm directly.

(a) Describe what these modifications would need to be.

(b) Using the Big M method, apply the modified algorithm developed in part (a) to solve the following problem directly by hand. (Do not use your OR Courseware.)

Minimize Z = 3x1 + 8x2 + 5x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

(a) Describe what these modifications would need to be.

(b) Using the Big M method, apply the modified algorithm developed in part (a) to solve the following problem directly by hand. (Do not use your OR Courseware.)

Minimize Z = 3x1 + 8x2 + 5x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

## Relevant Questions

Consider the following problem. Maximize Z = – 2x1 + x2 – 4x3 + 3x4, Subject to and x2 ≥ 0, x3 0, x4 ≥ 0 (no nonnegativity constraint for x1). (a) Reformulate this problem to fit our standard form for a linear ...Consider the following problem. Maximize z = x1 – 7x2 + 3x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Work through the simplex method step by step to solve the problem. (b) Identify the shadow prices for the three ...AmeriBank will soon begin offering Web banking to its customers. To guide its planning for the services to provide over the Internet, a survey will be conducted with four different age groups in three types of communities. ...Reconsider the model in Prob. 4.6-9. Now you are given the information that the basic variables in the optimal solution are x2 and x3. Use this information to identify a system of three constraint boundary equations whose ...The formula for the line passing through (2, 4, 3) and (4, 2, 4) in Fig. 5.2 can be written as (2, 4, 3) + α [(4, 2, 4) – (2, 4, 3)] = (2, 4, 3) + α (2, –2, 1), where 0 ≤ α ≤ 1 for just the line segment between ...Post your question