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1.2_Linear_Programming_-_Applications_of_LP_(Student)

1.2_Linear_Programming_-_Applications_of_LP_(Student) -...

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1 Linear Programming Part II: Applications of LP Chapter 4 2 Chapter Outline More Applications of LP Formulation (in complex problem situations) A Product Mix Example An Investment Example A Marketing Example A Blend Example A Multi-period Scheduling Example 3 A Product Mix Example Problem Definition (1 of 4) Four-product T-shirt/sweatshirt manufacturing company. Must complete all production within 72 hours Truck capacity for accommodating 1,200 standard-size boxes. A standard-size box holds 12 T-shirts. A box of 12 sweatshirts is three times the size of a standard box. $25,000 available for the production run. 500 dozen blank T-shirts and sweatshirts each in stock, ready for production Problem: How many dozens (boxes) of each type of shirt to produce for maximizing the total profit? 4 A Product Mix Example (2 of 4)
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5 Processing Time (hr) per dozen Cost ($) per dozen Profit ($) per dozen Sweatshirt - F 0.10 $36 $90 Sweatshirt - B/F 0.25 48 125 T-shirt - F 0.08 25 45 T-shirt - B/F 0.21 35 65 A Product Mix Example Data (3 of 4) 6 Decision Variables (x i in dozens): x 1 = sweatshirts, front printing x 2 = sweatshirts, back and front printing x 3 = T-shirts, front printing x 4 = T-shirts, back and front printing Objective Function: Maximize Z = 90x 1 + 125x 2 + 45x 3 + 65x 4 Model Constraints: 0.10x 1 + 0.25x 2 + 0.08x 3 + 0.21x 4 72 3x 1 + 3x 2 + x 3 + x 4 1,200 36x 1 + 48x 2 + 25x 3 + 35x 4 25,000 x 1 + x 2 500 x 3 + x 4 500 x i 0 A Product Mix Example Model Formulation (4 of 4) 7 Kathleen wants to invest the entire $70,000 among 4 alternatives: An Investment Example Data (1 of 4) Alternatives Annual Return Municipal bonds 8.5% Certificates of deposit (CDs) 5% Treasury bills 6.5% Growth stock funds 13% 8 An Investment Example
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