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Homework Examples

# Homework Examples - Product Mix A Product Mix Example...

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Product Mix Page 1 A Product Mix Example Products: X1 X2 X3 X4 Profit per box: 90 125 45 65 Resources: Usage processing time (hr/box) 0.1 0.25 0.08 0.21 72.0 shipping capacity (boxes) 3 3 1 1 1200.0 budget (\$/box) 36 48 25 35 21593.3 blank sweatshirts (boxes) 1 1 233.3 blank T-shirts (boxes) 1 1 500.0 Production: X1 = 175.56 sweatshirts, front printing X2 = 57.78 sweatshirts, back and front printing X3 = 500.00 T-shirts, front printing X4 = 0.00 T-shirts, back and front printing Profit = 45522.22 maximi subject

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Product Mix Page 2 Resources Constraints Available Left over <= 72 0.0 <= 1200 0.0 <= 25000 3406.7 <= 500 266.7 <= 500 0.0 ize Z = 90 x 1 + 125 x 2 + 45 x 3 + 65 x 4 t to: .1 x 1 + .25 x 2 + .08 x 3 + .21 x 4 <= 72 3 x 1 + 3 x 2 + x 3 + x 4 <= 1200 36 x 1 + 48 x 2 + 25 x 3 + 35 x 4 <= 25000 x 1 + x 2 <= 500 x 3 + x 4 <= 500 x 1, x 2, x 3, x 4 >= 0
Microsoft Excel 12.0 Answer Report Worksheet: [Chapter 4 examples.xlsx]Investment Report Created: 9/23/2010 12:46:52 PM Target Cell (Max) Cell Name Original Value Final Value \$B\$17 Z = 6618.18 6618.18 Adjustable Cells Cell Name Original Value Final Value \$B\$13 X1 = 0 0 \$B\$14 X2 = 0 0 \$B\$15 X3 = 38181.82 38181.82 \$B\$16 X4 = 31818.18 31818.18 Constraints Cell Name Cell Value Formula Status \$H\$6 1. municipal bonds Achievement 0.00 \$H\$6<=\$J\$6 Not Binding \$H\$7 2. CDs Achievement -70000.00 \$H\$7<=\$J\$7 Not Binding \$H\$8 3. treasury bills and CDs Achievement 38181.82 \$H\$8>=\$J\$8 Not Binding \$H\$9 4. ratio Achievement 0.00 \$H\$9>=\$J\$9 Binding \$H\$10 total invested Achievement 70000.00 \$H\$10=\$J\$10 Not Binding

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Slack 14000 70000 17181.82 0.00 0 8.5% is current return rate for x1. In order for x1 to app solution the return rate must increase by at lease 4.5%
pear in final % (

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Microsoft Excel 12.0 Sensitivity Report Worksheet: [Chapter 4 examples.xlsx]Investment Report Created: 9/23/2010 12:46:52 PM Adjustable Cells Final Reduced Objective Cell Name Value Cost Coefficient \$B\$13 X1 = 0 -0.04 0.09 \$B\$14 X2 = 0 -0.01 0.05 \$B\$15 X3 = 38181.82 0 0.07 \$B\$16 X4 = 31818.18 0 0.13 Constraints Final Shadow Constraint Cell Name Value Price R.H. Side \$H\$6 1. municipal bonds Achievement 0.00 0.00 14000 \$H\$7 2. CDs Achievement -70000.00 0.00 0 \$H\$8 3. treasury bills and CDs Achievement 38181.82 0.00 21000 \$H\$9 4. ratio Achievement 0.00 -0.03 0 \$H\$10 total invested Achievement 70000.00 0.09 70000
Allowable Allowable e more unit of X1 profit would decrease[reduce] by .0449999 Increase Decrease 0.04 1.00E+030 0.01 1.00E+030 0.06 0.01 45355.04 0.05 Allowable Allowable Increase Decrease 1.00E+030 14000 1.00E+030 70000 17181.82 1.00E+030 70000 37800 1.00E+030 31500 8.5% is current return rate for x1. In order for x1 solution the return rate must increase by at leas (4.5+8.5=13%) Shadow price of zero: increasing right hand side bond achievement would not increase returns Shadow price or .09: If you increase the allowabl \$70,000 profit will increase by 9 cents. The -70,000 for CD's achievement is like that be investment in the other investments

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1 to appear in final se 4.5% e value of Municial ble investment of ecause we had no
Investment Page 9 An Investment Example Investments: X1 X2 X3 X4 Rate of return: 0.09 0.05 0.07 0.13 Guidelines: Achievement 1. municipal bonds 1 0.00 2. CDs -1 1 -1 -1 -70000.00 3. treasury bills and CDs 1 1 38181.82 4. ratio -1.2 1 1 -1.2 0.00 total invested 1 1 1 1 70000.00 Returns: X1 = 0 invested in municipal bonds X2 = 0 invested in CDs X3 = 38181.82 invested in treasury bills X4 = 31818.18 invested in stock fund Z = 6618.18 total return m su

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Investment Page 10 Guidelines Constraints Requirements Slack/Surplus <= 14000.00 14000.00 <= 0.00 70000.00 >= 21000.00 17181.82 >= 0.00 0.00 = 70000.00 0.00 maximize Z = .085 x 1 + .050 x 2 + .065 x 3 + .130 x 4 ubject to: x 1 <= 14000 x 2 - x 1 - x 3 - x 4 <= 0 x 2 + x 3 >= 21000 -1.2 x 1 + x 2 + x 3 - 1.2 x 4 >= 0 x 1 + x 2 + x 3 + x 4 = 70000 x 1, x 2, x 3, x 4 >= 0