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3-4) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E + 30 3-5) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00  D) $158.18

3-4) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E + 30 3-5) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00  D) $158.18

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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3-4) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z?

A) 28.73

B) 39.27

C) 0

D) 1E + 30

3-5) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally?

A) $0

B) $9.09

C) $29.00 

D) $158.18



**Variable Cells** | Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease | |-------|------|-------------|--------------|-----------------------|-------------------|-------------------| | $C$4 | Z | 1.45 | 0 | 14 | 0.63 | 5.33 | | $D$4 | Y | 8.36 | 0 | 13 | 8 | 0.56 | | $E$4 | X | 0 | -0.818 | 17 | 0.818 | 1E+30 | **Constraints** | Cell | Name | Final Value | Shadow Price | Constraint R.H. Side | Allowable Increase | Allowable Decrease | |-------|--------|-------------|--------------|----------------------|-------------------|-------------------| | $F$6 | Beef | 28 | 0.45 | 28 | 2 | 10.22 | | $F$7 | Cheese | 80 | 1.45 | 80 | 46 | 5.33 | | $F$8 | Beans | 39.27 | 0 | 68 | 1E+30 | 28.73 | This table presents a linear programming solution summary that includes "Variable Cells" and "Constraints." **Variable Cells:** - Each cell is given a `Name` and associated values such as `Final Value`, `Reduced Cost`, and `Objective Coefficient`. - `Allowable Increase` and `Allowable Decrease` indicate the range within which the objective coefficient can change without affecting the current solution. **Constraints:** - Similarly, each constraint has a `Name`, `Final Value`, and is associated with a `Shadow Price`, which represents the change in the objective function per unit change in the right-hand side of the constraint. - The `Allowable Increase` and `Allowable Decrease` columns demonstrate the permissible limits for changing the right-hand side of each constraint without altering the basis of the solution.
Transcribed Image Text:**Variable Cells** | Cell | Name | Final Value | Reduced Cost | Objective Coefficient | Allowable Increase | Allowable Decrease | |-------|------|-------------|--------------|-----------------------|-------------------|-------------------| | $C$4 | Z | 1.45 | 0 | 14 | 0.63 | 5.33 | | $D$4 | Y | 8.36 | 0 | 13 | 8 | 0.56 | | $E$4 | X | 0 | -0.818 | 17 | 0.818 | 1E+30 | **Constraints** | Cell | Name | Final Value | Shadow Price | Constraint R.H. Side | Allowable Increase | Allowable Decrease | |-------|--------|-------------|--------------|----------------------|-------------------|-------------------| | $F$6 | Beef | 28 | 0.45 | 28 | 2 | 10.22 | | $F$7 | Cheese | 80 | 1.45 | 80 | 46 | 5.33 | | $F$8 | Beans | 39.27 | 0 | 68 | 1E+30 | 28.73 | This table presents a linear programming solution summary that includes "Variable Cells" and "Constraints." **Variable Cells:** - Each cell is given a `Name` and associated values such as `Final Value`, `Reduced Cost`, and `Objective Coefficient`. - `Allowable Increase` and `Allowable Decrease` indicate the range within which the objective coefficient can change without affecting the current solution. **Constraints:** - Similarly, each constraint has a `Name`, `Final Value`, and is associated with a `Shadow Price`, which represents the change in the objective function per unit change in the right-hand side of the constraint. - The `Allowable Increase` and `Allowable Decrease` columns demonstrate the permissible limits for changing the right-hand side of each constraint without altering the basis of the solution.
**Taco Loco** Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. **Objective Function:** Maximize Revenue (R) = 14Z + 13Y + 17X **Subject to Constraints:** - Beef: 2Z + 3Y + 4X ≤ 28 - Cheese: 9Z + 8Y + 11X ≤ 80 - Beans: 4Z + 4Y + 2X ≤ 68 **Non-Negativity Constraints:** - X, Y, Z ≥ 0 The sensitivity report from the computer model reads as follows: [The content of the sensitivity report would typically follow here, providing specific information about how changes in coefficients or right-hand side values might affect the optimal solution. Unfortunately, details of the sensitivity report aren't provided in the given image.]
Transcribed Image Text:**Taco Loco** Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. **Objective Function:** Maximize Revenue (R) = 14Z + 13Y + 17X **Subject to Constraints:** - Beef: 2Z + 3Y + 4X ≤ 28 - Cheese: 9Z + 8Y + 11X ≤ 80 - Beans: 4Z + 4Y + 2X ≤ 68 **Non-Negativity Constraints:** - X, Y, Z ≥ 0 The sensitivity report from the computer model reads as follows: [The content of the sensitivity report would typically follow here, providing specific information about how changes in coefficients or right-hand side values might affect the optimal solution. Unfortunately, details of the sensitivity report aren't provided in the given image.]
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