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ppt S_05- Linear Programming

# ppt S_05- Linear Programming - Operations Management...

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Operations Management Session 5:  Linear Programming

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Session 5 Operations Management 2 Previous Class Kristen Cookie Capacity Planning
Session 5 Operations Management 3 Today’s Class Understand what a Linear Program is. Understand how to solve small LP’s graphically. Practice LP formulation

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Session 5 Operations Management 4 What to produce? A computer manufacturer produces 2 types of  computers HS (High Speed) and LS (Low Speed).  The profit margin for HS computer is \$100 per unit  and for LS computer is \$75 per unit.  One assembling machine is used for both models.  The machine operates 600 minutes a day. A HS  unit needs 30 minutes, and A LS unit needs 10  minutes.
Session 5 Operations Management 5 What to produce? One testing machine is also used for both models. The machine operates 600 minutes a day. A HS unit needs 10 minutes and A LS unit needs  20 minutes.

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Session 5 Operations Management 6 What to produce? We also need a packaging machine.  The machine operates 600 min a day.  Every single product needs 20 min for packing.
Session 5 Operations Management 7 Solve Graphically LS HS 40 30 15 20 5 5 100*HS+75*LS = C (5,5) C=3000 C=1500

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Session 5 Operations Management 8 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600
Session 5 Operations Management 9 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600 10*HS+20*LS = 600 (24,12) 30

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Session 5 Operations Management 10 Solve Graphically LS HS 40 30 15 20 100*HS+75*LS = C 20 60 30*HS+10*LS = 600 10*HS+20*LS = 600 20*HS+20*LS = 600 (15,15) 30
Session 5 Operations Management 11 What to produce? x = # LS to produce; y = # HS to produce Maximize profit:  100y + 75x Assembly machine constraint: 30y + 10x <= 600 Testing machine constraint: 10y + 20x <= 600 Packaging machine constraint: 20y + 20x <= 600

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Session 5 Operations Management 12 Another Production Example A toy company offers 2 different dolls: Beauty and  Beast.  The daily demand for each doll is 400  units. There are two types of machines. Everyday, M1  can make 10 units of Beauty and 2 units of Beast;   M2 can make 3 units of Beauty and 7 units of  Beast.
Session 5 Operations Management 13 Another Production Example M1 costs \$7 K and M2 costs \$5 K. How many units of M1 and M2 should the  company purchase?

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Session 5 Operations Management 14 Another Production Example Demand                           Question      10 2 M1 3 7 M2 7 5 400 400 ? ?
Session 5 Operations Management 15 Another Production Example What should be the objective of the toy company?

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