00Production Plannning Models Homework Problem 1 09

00Production Plannning Models Homework Problem 1 09 - (1)...

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Unformatted text preview: (1) Numerical Instance. ' I Define any notation needed and formulate the followmg problem as a linear program. 7 A manufacturer produces a line of household products' fabricated from sheet metal. To illustrate his production planning problem,- suppose that he makes only four products and that his piroductiori system consists of five production centers: stamping, drilling, assembly, finishing (painting and printing), and packaging. For a given month, he must decide how much of each product to manufacture, and to aid in this decision, he has assembled the data shown in Tables 3-1 and 3-2. Furthermore, he knows that only 2000 square feet of the type of sheet metal used for products 2 and 4 will be available during the month. Prdduct 2 requires 2.0 square feet per unit and product 4 uses 1.2 square feet per unit. - TABLE 3—1 Production Data for Exampre 3-1 W PRODUCTION RATES IN HOURS PER UNIT PRODUCTION m HOURS DEPARTMENT PRODUCT‘I PRODUCT2 PRODUCTS PRODUCT4 AVAILABLE Stamping 0.03 0.15 0.05 0.10 ' 400 Drilling 0.06 0.12 — 0.10 . 400 Assembly ' 0.05 0.10 0.05 0.12 500 Finishing 0.04 0.20 0.03 0.12 450 Packaging 0.02 0.06 0.02 0.05 400 . TABLEa—z Product Data for Example 3-1 _ _ , ' ' . SALES POTEN IA 1 NET SELLING VARIABLE ~————————_.:_L___ 'anooucr PRICE/UNIT ' COST/UNIT MINIMUM ' MAXIMUM 7. 1 f - ‘ , $10 . $5 1000 I 6000 2 25 I 15 —— 500 H: 15 -- . 11 '500 3000 20 14 I 100. 1000 (1) Numerical Instance. I Define any notation needed and formulate the following problem as a lmear program. 7 A manufacturer produces a line of household products' fabricated from sheet metal. To illustrate his production planning problem, suppose that he makes only four products and that his ploductiorr system consists of five production centers: stamping, drilling, assembly, finishing (painting and printing), and packaging. For a given month, he must decide how much of each product to manufacture, and to aid in this decision, he has assembled the data shown in Tables 3-1 and 3-2. Furthermore, he knows that only 2000 square feet of the type of sheet metal used for products 2 and 4 will be available during the month. Product 2 requires 2.0 square feet per unit and product 4 uses 12 square feet per unit. - TABLE 3—1 Production Data for Example 3-1 m PRODUCTION RATES lN HOURS PER UNIT, PRODUCTION HOURS DEPARTMENT PRODUCT‘I PRODUCTZ PHODUCTB PRODUCT4 AVAILABLE Stamping 0.03 0.15 0.05 0.10 ' 400 - ’ Drilling 0.06 0.12 — 0.10 . 400 ' Assembly ' 0.05 0.10 0.05 0._12 500 Finishing 0.04 0.20 0.03 0.12 450 Packaging 0.02 0.06 0.02 0.05 400 . TABLE3-2 Product Data for Example 3-1 _ , , ' ' SALES POTEN IA . NET SELLING VAFliABLE __________;L___ 'snooucr PRICE/UNIT ‘ COST/UNIT MINIMUM ' MAXIMUM . 1 f p . $10 . so 1000 6000 2 25 I 15 —— 500 “‘3; 1s -- . 11 '500 3000 20 14 . 100. 1000 ...
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00Production Plannning Models Homework Problem 1 09 - (1)...

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