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Lecture3 - EM-602/QM-710(NJ Problem 28(homework Management...

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EM-602/QM-710 (NJ) Management Science Lecture 3 Simplex Method Problem 2-8 (cont’d) l Maximum of 800 Components I Day l Profit per unit of Model 1 is $30 l Proftt per unit of Model 2 is $20 l Determine the Optimum Daily Production for Each Model Radio Ka Problem 2-8 [email protected] Problem 28 (homework) l Electronics Co. Makes Two Modei Radios l Capacity of First Line is 60 Radios I Day l Capacity of Second Line is 75 Radios I DaY l Each unft of Model 1 uses 10 pcs. of a Component l Each unit of Mode4 2 uses 8 pcs. of the Same Component Problem 28 (SOkltiO~) . Lila . . Number of Units ofModel 1. 1 = .r,,x2 Maximize 2 = 30x, +20x, subject to x, 5 60 x2 I75 10x, +8x2 I 800 x,.x, t 0 Problem 2-l 1 (homework) Company produces 2 products, A and B Sales of A is at least 60% of total sales Both products use same raw material of which 100 ibs is available Product A uses 2 lb I unit - B uses 4 lb I unit Unit Selling prices for (A B) are $20 6.840 Find the optimal product mix EM-602 I QM-710 (NJ) Lecture 3 Page 3-l
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Problem 2-l 1 (Solution) Number ofUnits of Product A.B = I, .x2 Maslmize z = 20x, +40x, subject to -O.-lx, +0.6.r, 5 0 ‘s, +4x, 5 100 X,..‘c~ t 0 Problem 2-28 (homework) l Four Products produced on 2 machines l Mfg Times (hrs I unit) are given for each product and machine in the table below Machine Prod1 Prod2 Prod3 Prod4 TotHrS 1 2 3 4 2 500 2 3 2 1 2 380 l Cost per hour of machine (1, 2) is ($10, $5) l Sales price per unit is $65, $70, $55, and 646 l Formulate an LP to optimize total Net Protlt Problem 2-28 (SOlUtiOtl) Profit = Revenue - Expense Product 1: 30=65-[(Z)(lO)-(3)(j)] Product 2: 30 = 70-[(3X IO) -(Z)(j)] Product 3 lt~=jj-((-1X10)-(IXj)] Product-I Ij=-lj-((Z)(lO)-(2)(j)] , x, Problem 2-l 1 Problem 2-28 (Solution) Total of Products I. 2. 3. 4 = 5, .x1.x, .I, Maximize z = 30x, +30x2 +10x, +15x, s. t. 21, + 3.5 +4x, + 21, 5 500 3x, +2x, + I, + 2x, I 380 5, _.r> .I) .x1 2 0 Standard Form of LP A Linear Program is in standard form if: l
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