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Table 3.6 Taco LocoTaco 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.Max R = 14Z + 13Y + 17Xsubject to:Beef 2Z + 3Y + 4X ≤ 28Cheese 9Z + 8Y + 11X ≤ 80Beans 4Z + 4Y + 2X ≤ 68X,Y,Z ≥ 0The sensitivity report from the computer model reads as follows:What is the increase in revenue if Taco Loco purchases 36 pounds of additional cheese for $1.19 and uses it optimally? (Round to 2 decimal places)

Question

Table 3.6 Taco LocoTaco 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,aYfor17, a Y for 13, and a Z for 14.Thecompanysmanagementscienceconsultantformulatesthefollowinglinearprogrammingmodelforcompanymanagement.MaxR=14Z+13Y+17Xsubjectto:Beef2Z+3Y+4X28Cheese9Z+8Y+11X80Beans4Z+4Y+2X68X,Y,Z0Thesensitivityreportfromthecomputermodelreadsasfollows:WhatistheincreaseinrevenueifTacoLocopurchases36poundsofadditionalcheesefor14. The company's management science consultant formulates the following linear programming model for company management.Max R = 14Z + 13Y + 17Xsubject to:Beef 2Z + 3Y + 4X ≤ 28Cheese 9Z + 8Y + 11X ≤ 80Beans 4Z + 4Y + 2X ≤ 68X,Y,Z ≥ 0The sensitivity report from the computer model reads as follows:What is the increase in revenue if Taco Loco purchases 36 pounds of additional cheese for 1.19 and uses it optimally? (Round to 2 decimal places)

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Solution 1

To answer this question, we need to understand the concept of shadow price or dual value in linear programming. The shadow price represents the rate of change in the optimal value of the objective function per unit increase in the right-hand side of a constraint.

However, the sensitivity report, which usually contains the shadow prices, is not provided in the question. Therefore, we cannot directly calculate the increase in revenue from purchasing additional cheese.

If the shadow price for cheese was provided, we could multiply it by the increase in the amount of cheese (36 pounds) to find the increase in revenue.

Without this information, it's not possible to provide a numerical answer to this question.

This problem has been solved

Solution 2

To answer this question, we need to understand the concept of shadow price or dual value in linear programming. The shadow price represents the rate of change in the optimal value of the objective function per unit increase in the right-hand side of a constraint.

However, the sensitivity report, which usually contains the shadow prices, is not provided in the question. Therefore, without the shadow price for the cheese constraint, we cannot calculate the increase in revenue if Taco Loco purchases 36 pounds of additional cheese.

If the shadow price was provided, we would multiply it by the increase in the amount of cheese (36 pounds) to get the increase in revenue.

This problem has been solved

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