PROBLEMS, SECTION 14 Evaluate each of the following in r+iy form, and compare with a computer...
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PROBLEMS, SECTION 14 Evaluate each of the following in r+iy form, and compare with a computer solution. 1. In(-e) 2. In(-i) 3. In(i + √√3) 4. In(i-1) 5. In(-√√2-i√√2) 6. In ('1√2) 7. 8. 2/3 9. (-1) In i 10. i 11. 2' 13. 12/M 14. (21)+1 16. 17. (i-1)+1 19. cos(+iIn 2) 20. sin (i In 174) 12. 3+ 15. (-1) 18. cos(2i In i) 21. cos(i In(-1)] 3). For the following LP model, answer the questions Min. 8X 12Y s.t. and IX-3Y29 2X+2Y2 10 6X+2Y 218 X. Y20 a). Use the graphical solution procedure to find optimal solution. b). Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use graphical procedure to find new optimal solution. c). Assume that the objective function coefficient for X remains at 8 but, coefficient for Y changes from 12 to 6. Does the optimal solution change? Use graphical procedure to find new optimal solution. d). The computer solution for part (a) shows the following: Variable X Y Objective Coefficient 8.00000 12.00000 Allowable Increase Allowable Decrease 4.00000 12.00000 4.00000 4.00000 How would you interpret this objective coefficient range prior to re-solving the problem? e). Suppose that the RHS of constraint I has been increased from 9 to 10. Determine the dual value for constraint 1. Interpret this dual value using the following computer solution information. The computer solution provides the right-hand-side range information as: Constraint RHS Value 1 9.00000 2 10.00000 3 18.00000 Allowable Increase 2.00000 8.00000 4.00000 Allowable Decrease 4.00000 1.00000 Infinite f). If the dual value for constraint 2 is 3, what conclusion can be drawn about the effect of changes in right-hand-side of constraint 2? PROBLEMS, SECTION 14 Evaluate each of the following in r+iy form, and compare with a computer solution. 1. In(-e) 2. In(-i) 3. In(i + √√3) 4. In(i-1) 5. In(-√√2-i√√2) 6. In ('1√2) 7. 8. 2/3 9. (-1) In i 10. i 11. 2' 13. 12/M 14. (21)+1 16. 17. (i-1)+1 19. cos(+iIn 2) 20. sin (i In 174) 12. 3+ 15. (-1) 18. cos(2i In i) 21. cos(i In(-1)] 3). For the following LP model, answer the questions Min. 8X 12Y s.t. and IX-3Y29 2X+2Y2 10 6X+2Y 218 X. Y20 a). Use the graphical solution procedure to find optimal solution. b). Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use graphical procedure to find new optimal solution. c). Assume that the objective function coefficient for X remains at 8 but, coefficient for Y changes from 12 to 6. Does the optimal solution change? Use graphical procedure to find new optimal solution. d). The computer solution for part (a) shows the following: Variable X Y Objective Coefficient 8.00000 12.00000 Allowable Increase Allowable Decrease 4.00000 12.00000 4.00000 4.00000 How would you interpret this objective coefficient range prior to re-solving the problem? e). Suppose that the RHS of constraint I has been increased from 9 to 10. Determine the dual value for constraint 1. Interpret this dual value using the following computer solution information. The computer solution provides the right-hand-side range information as: Constraint RHS Value 1 9.00000 2 10.00000 3 18.00000 Allowable Increase 2.00000 8.00000 4.00000 Allowable Decrease 4.00000 1.00000 Infinite f). If the dual value for constraint 2 is 3, what conclusion can be drawn about the effect of changes in right-hand-side of constraint 2?
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