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lecture4-IE122

# lecture4-IE122 - IE 122 Lecture 4 Product Mix Example Part...

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IE 122 Lecture 4

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Product Mix Example: Part Name TV set Stereo Speaker inventory Chassis 1 1 0 450 Picture Tube 1 0 0 250 Speaker Cone 2 2 1 800 Power Supply 1 1 0 450 Electronics 2 1 1 600 Profit \$75 \$50 \$35 3 products: TV sets, stereos and speakers. 5 different parts: Chassis, picture tubes, speaker cones, power supplies and electronics units. Produce the mix of products to maximize profits, given the inventory of products on hand.
LP model for Product Mix Example: Decision variables: X_TV= the number of TV sets assembled, X_STEREO= the number of stereos, and X_SPEAKER= the number of speakers Objective Function: Our goal is to maximize the total gross profit. Maximize 75 x_TV + 50 x_STEREO + 35 x_SPEAKER (Profit) Constraints: Subject to: 1 x_TV + 1 x_STEREO + 0 x_SPEAKER <= 450 (Chassis) 1 x_TV + 0 x_STEREO + 0 x_SPEAKER <= 250 (Picture tubes) 2 x_TV + 2 x_STEREO + 1 x_SPEAKER <= 800 (Speaker cones) 1 x_TV + 1 x_STEREO + 0 x_SPEAKER <= 450 (Power supplies) 2 x_TV + 1 x_STEREO + 1 x_SPEAKER <= 600 (Electronics) x _TV >=0, x _STEREO >=0, x _SPEAKER >=0 (No negativity)

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Sets In our model: Product Set={TV sets ,stereos, speakers} Part Set={Chassis, picture tubes, speaker cones, power supplies, electronics units} Defining in ampl: set Products; set Parts;
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