331-05 - Chapter 3: Linear Programming Modeling...

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Chapter 3: Linear Programming Modeling Applications with Computer Analysis in Excel
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LP Applications for Managerial Decisions Manufacturing Marketing Finance Employee staffing Logistics Operations Multiperiod planning
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Modeling and Solving with LPs Define the decision variables Formulate the LP model using the decision variables Write the objective function Write each of the constraint equations/inequalities Implement the model in Excel Solve using Excel Solver
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Manufacturing Application: Product Mix Problem Produce 4 types of men's ties Use 3 materials (limited resources) Decisions: How many of each type of tie to make per month? Objective: Maximize profit Fifth Avenue_Industries
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Material Cost per yard Yards available per month Silk $20 1,000 Polyester $6 2,000 Cotton $9 1,250 Resource Data Resource Data Labor cost is $0.75 per tie (of any type)
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Product Data Type of Tie Silk Polyester Blend 1* Blend 2* Selling Price (per tie) $6.70 $3.55 $4.31 $4.81 Monthly Minimum 6,000 10,000 13,000 6,000 Monthly Maximum 7,000 14,000 16,000 8,500 * Blends 1 and 2 are different mixtures of  polyester and cotton. 
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Material Requirements (yards per tie) Material Type of Tie Silk Polyester Blend 1 Blend 2 Silk 0.125 0 0 0 Polyester 0 0.08 0.05 0.03 Cotton 0 0 0.05 0.07
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Decision Variables S = number of silk ties to make per month P = number of polyester ties to make per month B 1 = number of poly-cotton blend 1 ties to make per month B 2 = number of poly-cotton blend 2 ties to make per month
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Profit Per Tie Calculation (REVISED) Profit per tie = (selling price) – (material cost) –(labor cost) Silk Tie Profit = $6.70 – (0.125 yds)($20/yd) - $0.75 = $3.45 per tie Polyester Tie Profit = $3.55 – (0.08 yds)($6/yd) - $0.75 = $2.32 per tie
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331-05 - Chapter 3: Linear Programming Modeling...

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