Suppose the price of a BR increases from 50 to 60 and the price of a PC decreases from 80 to 50. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)? Suppose the price of a BR increases from 50 to 70 and the price of a PC increases from 80 to 90. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)? How much would you pay for an additional unit of Resource 2 (Constraint 2)? Suppose you were to acquire 150 additional units of Resource 1 (Constraint 1), what would your new objective value be?
Suppose the price of a BR increases from 50 to 60 and the price of a PC decreases from 80 to 50. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)? Suppose the price of a BR increases from 50 to 70 and the price of a PC increases from 80 to 90. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)? How much would you pay for an additional unit of Resource 2 (Constraint 2)? Suppose you were to acquire 150 additional units of Resource 1 (Constraint 1), what would your new objective value be?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...
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Given the following output for the optimal solution for a 4 variable (named BR, IC, COLA, and PC) and a 4 resource (constraint) problem; where the optimal objective function value is 1000 (and it is a maximization problem). Please write a short summary that answers the following questions:
- Suppose the price of a BR increases from 50 to 60 and the price of a PC decreases from 80 to 50. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)?
- Suppose the price of a BR increases from 50 to 70 and the price of a PC increases from 80 to 90. Does the current solution remain optimal (in terms of the variables > 0 in the optimal solution)?
- How much would you pay for an additional unit of Resource 2 (Constraint 2)?
- Suppose you were to acquire 150 additional units of Resource 1 (Constraint 1), what would your new objective value be?
In your follow-up posts please clarify any issues or justify your answers.
Variable Cells
| Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease |
| $B$2 | Variabies BR | 0 | -30 | 50 | 30 | 1E+30 |
| $C$2 | Variables IC | 0 | -20 | 20 | 20 | 1E+30 |
| $D$2 | Variables COLA | 33.333333 | 0 | 30 | 1E+30 | 6 |
| $E$2 | VariabiesPC | 0 | -20 | 80 | 20 | 1E+30 |
Constraints
| Cell | Name | Final Value | Shadow Price | Constraint R.H. Side | Allowable Increase | Allowable Decrease |
| $F$5 | Resource 1 | 500 | 2 | 500 | 1E+30 | 380 |
| $F$6 | Resource 2 | 0 | 0 | 6 | 1E+30 | 6 |
| $F$7 | Resource 3 | 133.33333 | 0 | 10 | 123.3333333 | 1E+30 |
| $F$8 | Resource 4 | 33.333333 | 0 | 8 | 25.33333333 | 1E+30 |
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