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3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds

3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds

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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3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is:

A) 28 beef, 80 cheese, and 39.27 beans for $147.27.

B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27.

C) 1.45 Z, 8.36 Y, and 0 Z for $129.09.

D) 14 Z, 13 Y, and 17 X for $9.81.

3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix?

A) 26 to 38.22 pounds

B) 27.55 to 28.45 pounds

C) 17.78 to 30 pounds

D) 12.22 to 28 pounds



**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:** Maximize Revenue (R) = 14Z + 13Y + 17X **Subject to Constraints:** 1. Beef constraint: 2Z + 3Y + 4X ≤ 28 2. Cheese constraint: 9Z + 8Y + 11X ≤ 80 3. Beans constraint: 4Z + 4Y + 2X ≤ 68 4. Non-negativity restriction: X, Y, Z ≥ 0 The sensitivity report from the computer model reads as follows: [Details of the sensitivity report would be provided here if available]
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:** Maximize Revenue (R) = 14Z + 13Y + 17X **Subject to Constraints:** 1. Beef constraint: 2Z + 3Y + 4X ≤ 28 2. Cheese constraint: 9Z + 8Y + 11X ≤ 80 3. Beans constraint: 4Z + 4Y + 2X ≤ 68 4. Non-negativity restriction: X, Y, Z ≥ 0 The sensitivity report from the computer model reads as follows: [Details of the sensitivity report would be provided here if available]
### Variable Cells This table presents the details of three variable cells, featuring their final values, reduced costs, objective coefficients, and allowable ranges of increase or decrease. | 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 The following table highlights constraints related to three types of resources. It includes their final values, shadow prices, right-hand side constants, and allowable changes. | 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 | These tables illustrate the sensitivity analysis results in a linear programming context, summarizing how changes in variable values and constraints affect the solution.
Transcribed Image Text:### Variable Cells This table presents the details of three variable cells, featuring their final values, reduced costs, objective coefficients, and allowable ranges of increase or decrease. | 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 The following table highlights constraints related to three types of resources. It includes their final values, shadow prices, right-hand side constants, and allowable changes. | 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 | These tables illustrate the sensitivity analysis results in a linear programming context, summarizing how changes in variable values and constraints affect the solution.
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