HW 8 Solution

# HW 8 Solution - CSA 273 Homework Set#8 Solutions Problem#1...

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CSA 273 Homework Set #8 Solutions Problem #1 Raw Material Product A Product B Product C Availability I 7 lb 6 lb 3 lb 100 pounds II 5 lb 4 lb 2 lb 200 pounds Profits \$20 \$20 \$15 Let x 1 = Pounds of Product A to be produced x 2 = Pounds of Product B to be produced x 3 = Pounds of Product C to be produced Maximize total profit = 20x 1 + 20x 2 + 15x 3 7x 1 + 6x 2 + 3x 3 100 (Availability of Raw Material I) 5x 1 + 4x 2 + 2x 3 200 (Availability of Raw Material II) x i 0 for i=1,2,3 Standard form Basic Variables Row 0 z - 20x 1 - 20x 2 - 15x 3 = 0 z = 0 Row 1 7x 1 + 6x 2 + 3x 3 + s 1 = 100 s 1 = 100 Row 2 5x 1 + 4x 2 + 2x 3 +s 2 = 200 s 2 = 200 Initial Simplex Tableau Ratio z x 1 x 2 x 3 s 1 s 2 RHS BV Test 1 -20 -20 -15 0 0 0 z=0 0 7 6 3 1 0 100 s 1 =100 100/7 0 5 4 2 0 1 200 s 2 =200 200/5=40 x 1 enter basis, by ratio test s 1 becomes nonbasic. The pivot row is Row 1 and the pivot element is 7 Divide pivot row 1 by 7 z x 1 x 2 x 3 s 1 s 2 RHS 1 -20 -20 -15 0 0 0 0 1 6/7 3/7 1/7 0 100/7 0 5 4 2 0 1 200 New row 0 = old row 0 + 20*Pivot Row 1 New row 2 = old row 2 –5*Pivot Row 1 z x 1 x 2 x 3 s 1 s 2 RHS BV Ratio Test 1 0 -20/7 -45/7 20/7 0 2000/7 z=2000/7 0 1 6/7 3/7 1/7 0 100/7 x 1 =100/7 (100/7)/(3/7)=100/3 0 0 -2/7 -1/7 -5/7 1 900/7 s 2 =900/7 Not Applicable This bfs is not optimal since row 0 contains non-basic variables having negative

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HW 8 Solution - CSA 273 Homework Set#8 Solutions Problem#1...

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