# Ch.4 - Chapter 4 Linear Programming Modeling Examples BIT...

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Chapter 4 Linear Programming: Modeling Examples BIT 2406 1

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Chapter Topics A Product Mix Example A Diet Example An Investment Example A Marketing Example A Transportation Example A Blend Example A Multi-Period Scheduling Example BIT 2406 2
A Product Mix Example:Problem A Product Mix Example:Problem Definition Definition Quick-Screen is a clothing manufacturing company that specializes in producing commemorative shirts immediately following major sporting events such as the World Series and the Super Bowl. The company has been contracted to produce a standard set of shirts for the winning team of a college football game on New Years. The items produced include two sweatshirts, one with silk-screen printing on the front and one with print on both sides, and two T- shirts of the same configuration. The company has to complete production within 72 hours after the game, at which time a trailer truck will pick up the shirts. The company will work around the clock. The truck has enough capacity to accommodate 1,200 standard- size boxes. A standard-size box holds 12 T-shirts, and a box of 12 sweatshirts is three times the size of a standard box. The company has budgeted \$25,000 for the production run. It has 500 dozen blank sweatshirts and T-shirts each in stock, ready for production. BIT 2406 3

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A Product Mix Example: Problem Definition Four-product T-shirt/sweatshirt manufacturing company. Must complete production within 72 hours Truck capacity = 1,200 standard sized boxes. Standard size box holds12 T-shirts. One-dozen sweatshirts box is three times size of standard box. \$25,000 available for a production run. 500 dozen blank T-shirts and sweatshirts in stock. How many dozens (boxes) of each type of shirt to produce? BIT 2406 4
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A Product Mix Example: Data BIT 2406 6 SF SB TF TB RHS profit (\$) per dozen 90 125 45 65 Z processing time (hr) per dozen 0.1 0.25 0.08 0.21 72 Space (#) standard box 3 3 1 1 1200 cost (\$) per dozen 36 48 25 35 2500 0 Blank S 1 1 0 0 500 Blank T 0 0 1 1 500
A Product Mix Example: Model Construction BIT 2406 7 Decision Variables: 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 hr 3x 1 + 3x 2 + x 3 + x 4 1,200 boxes \$36x 1 + \$48x 2 + \$25x 3 + \$35x 4 \$25,000 x 1 + x 2 500 dozen sweatshirts x 3 + x 4 500 dozen T-shirts

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Product Mix Example Spreadsheet Setup for Solver BIT 2406 8
Product Mix Example Formula View BIT 2406 9

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Product Mix Example: Solver Setup BIT 2406 10
Product Mix: Solver Options and Results BIT 2406 11

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Product Mix: Solution BIT 2406 12
Product Mix: Sensitivity Analysis Report BIT 2406 13

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A Diet Example: Problem Definition Breathtakers, a health and fitness center, operates a morning fitness program for senior citizens. The program includes aerobic
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Ch.4 - Chapter 4 Linear Programming Modeling Examples BIT...

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