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This 2 page Class Notes was uploaded by Hali Nepsha on Friday October 14, 2016. The Class Notes belongs to BUSM 360 at Purdue University Calumet taught by Dr. Raida Abuizam in Fall 2016. Since its upload, it has received 2 views. For similar materials see Production/ Operations Management in Business at Purdue University Calumet.
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Date Created: 10/14/16
Busm 360 Formulating Linear Programming Model Step 1. Determine decision Variables Step 2. Determine Criteria Function Step 3. Determine Constraints Example: Sporting Goods acquired a new facility. This new facility has 10,00 square feet of display area. Sporting Goods has four products considered for display: Product A costs $55, sells for $80 and requires 24 square feet per unit for storage. Product B costs $100, sells for $130, and requires 20 square feet for storage. Product C costs $200, sells for $295 and requires 36 square feet for storage. Product D costs $300, sells for $399 and requires 50 square feet for storage. At least 10 units of each product are required to be displayed. The budget is set at $600,000 to purchase the products. How man units of each product should be on display to maximize profit contribution? Step 1. There are 4 products & it must be determined how much of each to acquire. Let X Ae the quantity of A to purchase, XBthe quantity of B to purchase, XCthe quantity of C to purchase, and X the quantity of D to purchase. D Step 2. The objective is to maximize profit contribution, so determine the profit contribution from each product. Product A: costs $55 and sells for $80. The profit contribution is $25 per unit. Product B: costs $100 and sells for $130. The profit contribution is $30 per unit. Product C: costs $200 and sells for $295. The profit contribution is $95 per unit. Product D: costs $300 and sells for $399. The profit contribution is $99 per unit. The profit contribution is stated as this linear function: Z = 25X +A30 X + 9BX + 99XC D Step 3. The constraints are the amount of storage space and the policy requiring minimum quantities. State these as linear expressions: For storage space: 24X A 20 X + B6X + 50XC≤ 10,00D For the minimum of 10 units per product policy: X A 10, X ≥ B0, X ≥ 10C X ≥ 10 D Maximize Z = 25X + 30 X + 95X + 99X A B C D Subject to these constraints: 24X A 20 X + B6X + 50XC≤ 10,00D X A 10, XB≥ 10, X ≥ 10, C XD≥ 10