Chapter 4.CRE, Problem 25CRE

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12th Edition

Soo T. Tan

ISBN: 9781337405782

Textbook Problem

**MAXIMIZING PROFIT **A company manufactures three products,

To determine

**To find:**

The number of units of each product to be produced in each shift to maximize the gains.

Explanation

**Given:**

A company manufactures three products,

**Approach:**

The Simplex Method for Solving Non-standard Problems

1. If necessary, rewrite the problem as a maximization problem (recall that minimizing

2. If necessary, rewrite all constraints (except

3. Introduce slack variables and set up the initial simplex tableau.

4. Scan the upper part of the column of constants of the tableau for negative entries.

a. If there are no negative entries, complete the solution using the simplex method for problems in standard form.

b. If there are negative entries, proceed to Step 5.

5. a. Pick any negative entry in a row in which a negative entry in the column of constants occurs. The column containing this entry is the pivot column.

b. Compute the positive ratios of the numbers in the column of constants to the corresponding numbers in the pivot column (above the last row). The pivot row corresponds to the smallest ratio. The intersection of the pivot column and the pivot row determines the pivot element.

c. Pivot the tableau about the pivot element. Then return to Step 4.

**Calculation:**

Let

Maximize

subject to

Introduce the slack variables

Base | |||||||

The leaving variable is

Sect-4.1 P-1CQSect-4.1 P-2CQSect-4.1 P-3CQSect-4.1 P-1ESect-4.1 P-2ESect-4.1 P-3ESect-4.1 P-4ESect-4.1 P-5ESect-4.1 P-6ESect-4.1 P-7E

Sect-4.1 P-8ESect-4.1 P-9ESect-4.1 P-10ESect-4.1 P-11ESect-4.1 P-12ESect-4.1 P-13ESect-4.1 P-14ESect-4.1 P-15ESect-4.1 P-16ESect-4.1 P-17ESect-4.1 P-18ESect-4.1 P-19ESect-4.1 P-20ESect-4.1 P-21ESect-4.1 P-22ESect-4.1 P-23ESect-4.1 P-24ESect-4.1 P-25ESect-4.1 P-26ESect-4.1 P-27ESect-4.1 P-28ESect-4.1 P-29ESect-4.1 P-30ESect-4.1 P-31ESect-4.1 P-32ESect-4.1 P-33ESect-4.1 P-34ESect-4.1 P-35ESect-4.1 P-36ESect-4.1 P-37ESect-4.1 P-38ESect-4.1 P-39ESect-4.1 P-40ESect-4.1 P-41ESect-4.1 P-42ESect-4.1 P-43ESect-4.1 P-44ESect-4.1 P-45ESect-4.1 P-46ESect-4.1 P-47ESect-4.1 P-48ESect-4.1 P-49ESect-4.1 P-50ESect-4.1 P-51ESect-4.1 P-52ESect-4.1 P-53ESect-4.1 P-54ESect-4.1 P-55ESect-4.1 P-1TESect-4.1 P-2TESect-4.1 P-3TESect-4.1 P-4TESect-4.2 P-1CQSect-4.2 P-2CQSect-4.2 P-3CQSect-4.2 P-4CQSect-4.2 P-1ESect-4.2 P-2ESect-4.2 P-3ESect-4.2 P-4ESect-4.2 P-5ESect-4.2 P-6ESect-4.2 P-7ESect-4.2 P-8ESect-4.2 P-9ESect-4.2 P-10ESect-4.2 P-11ESect-4.2 P-12ESect-4.2 P-13ESect-4.2 P-14ESect-4.2 P-15ESect-4.2 P-16ESect-4.2 P-17ESect-4.2 P-18ESect-4.2 P-19ESect-4.2 P-20ESect-4.2 P-21ESect-4.2 P-22ESect-4.2 P-23ESect-4.2 P-24ESect-4.2 P-25ESect-4.2 P-26ESect-4.2 P-27ESect-4.2 P-28ESect-4.2 P-29ESect-4.2 P-1TESect-4.2 P-2TESect-4.2 P-3TESect-4.2 P-4TESect-4.3 P-1CQSect-4.3 P-2CQSect-4.3 P-3CQSect-4.3 P-1ESect-4.3 P-2ESect-4.3 P-3ESect-4.3 P-4ESect-4.3 P-5ESect-4.3 P-6ESect-4.3 P-7ESect-4.3 P-8ESect-4.3 P-9ESect-4.3 P-10ESect-4.3 P-11ESect-4.3 P-12ESect-4.3 P-13ESect-4.3 P-14ESect-4.3 P-15ESect-4.3 P-16ESect-4.3 P-17ESect-4.3 P-18ESect-4.3 P-19ESect-4.3 P-20ESect-4.3 P-21ESect-4.3 P-22ESect-4.3 P-23ESect-4.3 P-24ESect-4.3 P-25ESect-4.3 P-26ESect-4.3 P-27ESect-4.3 P-28ESect-4.CRQ P-1CRQSect-4.CRQ P-2CRQSect-4.CRQ P-3CRQSect-4.CRQ P-4CRQSect-4.CRE P-1CRESect-4.CRE P-2CRESect-4.CRE P-3CRESect-4.CRE P-4CRESect-4.CRE P-5CRESect-4.CRE P-6CRESect-4.CRE P-7CRESect-4.CRE P-8CRESect-4.CRE P-9CRESect-4.CRE P-10CRESect-4.CRE P-11CRESect-4.CRE P-12CRESect-4.CRE P-13CRESect-4.CRE P-14CRESect-4.CRE P-15CRESect-4.CRE P-16CRESect-4.CRE P-17CRESect-4.CRE P-18CRESect-4.CRE P-19CRESect-4.CRE P-20CRESect-4.CRE P-21CRESect-4.CRE P-22CRESect-4.CRE P-23CRESect-4.CRE P-24CRESect-4.CRE P-25CRESect-4.CRE P-26CRESect-4.BMO P-1BMOSect-4.BMO P-2BMOSect-4.BMO P-3BMOSect-4.BMO P-4BMOSect-4.BMO P-5BMO

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