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The FastMart convenience store is deciding on the optimal mix of the number of 2-liter bottles of Sprite, 7-Up, and FM Citrus (its own brand) to stock on its shelves each week. The contribution margin of Sprite is $.69/bottle, of 7-Up is $.83/bottle, and of FM Citrus is $.97/bottle. The amount of shelf space available is 36 square feet (equal to 5,184 square inches) for all of these bottles, and each bottle takes up 16 square inches. In a given week, FastMart sells at least as much Sprite as it does 7- Up and FM Citrus combined. It also sells at least 3 times as much Sprite as it does FM Citrus each week. The 7-Up delivery truck can deliver a maximum of 120 bottles of 7-Up each week. Formulate an LP to determine how many bottles of the 3 soft drinks should be purchased each week in order to maximize total contribution margin. What is your optimal solution and the resulting objective function value? If FastMart could increase the shelf space for these drinks, how beneficial would that be? What limits exist for your answer to be valid? Should FastMart request the 7-Up bottling plant to deliver more 7-Up bottles each week? If so, what is it worth? If not, why not?

The FastMart convenience store is deciding on the optimal mix of the number of 2-liter bottles of Sprite, 7-Up, and FM Citrus (its own brand) to stock on its shelves each week. The contribution margin of Sprite is $.69/bottle, of 7-Up is $.83/bottle, and of FM Citrus is $.97/bottle. The amount of shelf space available is 36 square feet (equal to 5,184 square inches) for all of these bottles, and each bottle takes up 16 square inches. In a given week, FastMart sells at least as much Sprite as it does 7- Up and FM Citrus combined. It also sells at least 3 times as much Sprite as it does FM Citrus each week. The 7-Up delivery truck can deliver a maximum of 120 bottles of 7-Up each week. Formulate an LP to determine how many bottles of the 3 soft drinks should be purchased each week in order to maximize total contribution margin. What is your optimal solution and the resulting objective function value? If FastMart could increase the shelf space for these drinks, how beneficial would that be? What limits exist for your answer to be valid? Should FastMart request the 7-Up bottling plant to deliver more 7-Up bottles each week? If so, what is it worth? If not, why not?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 50P
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The FastMart convenience store is deciding on the optimal mix of the number of 2-liter bottles of Sprite, 7-Up, and FM Citrus (its own brand) to stock on its shelves each week. The contribution margin of Sprite is $.69/bottle, of 7-Up is $.83/bottle, and of FM Citrus is $.97/bottle. The amount of shelf space available is 36 square feet (equal to 5,184 square inches) for all of these bottles, and each bottle takes up 16 square inches. In a given week, FastMart sells at least as much Sprite as it does 7- Up and FM Citrus combined. It also sells at least 3 times as much Sprite as it does FM Citrus each week. The 7-Up delivery truck can deliver a maximum of 120 bottles of 7-Up each week. Formulate an LP to determine how many bottles of the 3 soft drinks should be purchased each week in order to maximize total contribution margin. What is your optimal solution and the resulting objective function value? If FastMart could increase the shelf space for these drinks, how beneficial would that be? What limits exist for your answer to be valid? Should FastMart request the 7-Up bottling plant to deliver more 7-Up bottles each week? If so, what is it worth? If not, why not?
Transcribed Image Text:The FastMart convenience store is deciding on the optimal mix of the number of 2-liter bottles of Sprite, 7-Up, and FM Citrus (its own brand) to stock on its shelves each week. The contribution margin of Sprite is $.69/bottle, of 7-Up is $.83/bottle, and of FM Citrus is $.97/bottle. The amount of shelf space available is 36 square feet (equal to 5,184 square inches) for all of these bottles, and each bottle takes up 16 square inches. In a given week, FastMart sells at least as much Sprite as it does 7- Up and FM Citrus combined. It also sells at least 3 times as much Sprite as it does FM Citrus each week. The 7-Up delivery truck can deliver a maximum of 120 bottles of 7-Up each week. Formulate an LP to determine how many bottles of the 3 soft drinks should be purchased each week in order to maximize total contribution margin. What is your optimal solution and the resulting objective function value? If FastMart could increase the shelf space for these drinks, how beneficial would that be? What limits exist for your answer to be valid? Should FastMart request the 7-Up bottling plant to deliver more 7-Up bottles each week? If so, what is it worth? If not, why not?
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