#8

 

Mgmt 380

 

Assignment #4

The Simplex method

 

DUE:Tuesday, March 13

15 points

 

 

A clothing store makes suits and blazers.Three main resources are used:material, rack space, and labor.The shop has developed this linear programming model for determining the number of suits and blazers to make in order to maximize profits:

 

 

X1 = number of suits to make

X2 = number of blazers to make

 

Zmax = $100X1 + $150X2†† (profit, $)

 

Subject to:

10X1 + 4X2 <=160†† (material, square yds.)

X1 + X2 <= 20†† (rack space)

10X1 + 20X2 <= 300†† (labor, hr)

X1,X2 >= 0

 

 

Transform the constraints into equations.

 

 

 

 

 


PART 1:Solve this model with the graphical method.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

What are the feasible solutions?

 

 

 

 

 

 

 

 

 

 

 

 

What is the optimal solution?

 

 

 

 


PART 2:Solve this model with the Simplex method

 

 

 

Simplex Tableau for this Model

1st Iteration

 

 

 

 

 

 

 

 

 

Cj

Basic

Variables

Quantity

(RHS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Zj

 

 

 

 

 

 

 

Cj - Zj

 

 

 

 

 

 

 

 

 

 

Simplex Tableau for this Model

2nd Iteration

 

 

 

 

 

 

 

 

 

Cj

Basic

Variables

Quantity

(RHS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Zj

 

 

 

 

 

 

 

Cj - Zj

 

 

 

 

 

 

 


 

Simplex Tableau for this Model

3rd Iteration

 

 

 

 

 

 

 

 

 

Cj

Basic

Variables

Quantity

(RHS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Zj

 

 

 

 

 

 

 

Cj - Zj

 

 

 

 

 

 

 

 

PART 3:Solve this model with STORM.

 

 

Attach your STORM printout and your memo to management to these papers.(Donít forget the cover sheet for your assignment.)

 

Include the following in your memo to management:

††††††††††† -problem description (why are you writing the memo)

-solution you are recommending to management.Look at all the information provided in the 3 ways you solved this problem, and report what is pertinent to managementís decision.