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Finding optimal solution using simplex method

A manufacturing company makes three types of office chairs: Model A, Model B, and Model C. The construction of each chair requires a process involving three departmental steps; material workup, assembly, and packaging. The three departments have a maximum of 30, 53, and 47 hours available each week, respectively. The information is summarized (show all steps please)

Model A Model B Model C
Material Workup (hrs) 1 1 1
Assembly (hrs) 2 3 2
Packaging (hrs) 1 2 3

a) Determine the objective function.

b) Introduce slack variables and set up the initial simplex tableau.

c) Solve the system (please show all steps)

d) Report your solutions in terms of maximum profit and each variable.

Solution Preview

a) Determine the objective function.
Let x, y and z be number of chairs of Model A, Model B, and Model C respectively and p be the total profits.
Objective function: Maximize p = 40x+80y+70z
Subject to: x + y + z <= 30
2x + 3y + 2z <= 53
x + 2y + 3z <= 47

b) Introduce slack variables and set up the initial simplex tableau.
Slack variables are s1, s2 and s3 correponding to Model A, Model B, and Model C respectively.
THe first table is:
Step ...

Solution Summary

The solution gived detailed steps on linear programming. All formula and calculations are shown and explained.

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