Problem #3: [35 pts] This problem is not a modeling problem. This problem is a S

Question

Problem #3: [35 pts] This problem is not a modeling problem. This problem is a Simplex Method solution problem. The scenario description is given here for context related to the final question Scenario: A manufacturer of picture frames would like to find a profit-optimal production plan for this week's production schedule. The machinery is tooled for the production of any combination of three types of frames. Each type of frame requires a certain quantity of wood, glass panes and machine time There are 320 hours of machine time, 200 feet of framing wood and 150 glass panes available. The profit and resource requirements for each type of frame are given in the following table.

Explanation / Answer

Find Solution Using Simplex Method

Problem is

Entering =X3=X3, Departing =S1=S1, Key Element = 22

R1R1 (new) =R1=R1 (old) ÷2=R1÷2=R1 (old) 1212

R2R2 (new) =R2=R2 (old) 2R1-2R1 (new)

R3R3 (new) =R3=R3 (old) 2R1-2R1 (new)

Entering =X2=X2, Departing =S2=S2, Key Element = 11

R2R2 (new) =R2=R2(old)

R1R1 (new) =R1=R1 (old) 12R2-12R2 (new)

R3R3 (new) =R3=R3 (old) 2R2-2R2 (new)

Since all CjZj0Cj-Zj0,

Optimum Solution is arrived with value of variables as :
X1=0X1=0

X2=50X2=50

X3=50X3=50

Maximise Z=2500

MAX Z=Z= 1010 X1+X1+ 2020 X2+X2+ 3030 X3X3 Subject to constraints 11 X1+X1+ 11 X2+X2+ 22 X3X3 150150 88 X1+X1+ 22 X2+X2+ 22 X3X3 200200 11 X1+X1+ 33 X2+X2+ 22 X3X3 320320 and X1,X2,X30X1,X2,X30

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