Zokit Industries (ZI) is a New York City based company that manufactures and distributes Turkish Delight to grocery chains in New York and New Jersey. The product line includes two main flavors: Ortaköy (O) and Beyoglu (B). Each flavor is sold in standard 10 oz. boxes. The table below shows ZI’s profit contribution from each flavor (in $ per box). Flavor Profit per box ($) O 5 B 5.3 Given the relatively small size of the market for Turkish delight, ZI cannot sell more than 250 boxes of Ortaköy, and more than 400 boxes of Beyoglu in the coming week. Both flavors use the following set of main ingredients with limited supply: starch, sugar, and fruit juice. Each flavor also uses other ingredients, such as gelatin, pectin, etc., but ZI has an essentially unlimited supply of those ingredients. For the coming week, the amounts of the three main ingredients the company has in storage are as follows: Ingredient  Availability  Starch 150 lbs Sugar 130 lbs Fruit juice 15 gallons The Ortaköy and Beyoglu flavors use the following amounts of the main ingredients (per box): Flavor   Starch (lbs) Sugar (lbs) Fruit juice (gallons) O 0.1 0.05 0.03 B 0.3 0.1 0.02 The company needs to decide how many boxes of each flavor to make during the coming week to maximize its weekly profit without exceeding the availabilities of the ingredients or the size of the Turkish delight market. Let NO be a decision variable that expresses the number of boxes of the Ortaköy flavor to make during the coming week, and let NB be a decision variable that expresses the number of boxes of the Beyoglu flavor to make during the coming week. Suppose that ZI decides to make 250 boxes of Ortaköy and 350 boxes of Beyoglu. What is the weekly profit that it will earn?

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
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Zokit Industries (ZI) is a New York City based company that manufactures and distributes Turkish Delight to grocery chains in New York and New Jersey. The product line includes two main flavors: Ortaköy (O) and Beyoglu (B). Each flavor is sold in standard 10 oz. boxes. The table below shows ZI’s profit contribution from each flavor (in $ per box).

Flavor Profit per box ($)
O 5
B 5.3

Given the relatively small size of the market for Turkish delight, ZI cannot sell more than 250 boxes of Ortaköy, and more than 400 boxes of Beyoglu in the coming week.

Both flavors use the following set of main ingredients with limited supply: starch, sugar, and fruit juice. Each flavor also uses other ingredients, such as gelatin, pectin, etc., but ZI has an essentially unlimited supply of those ingredients. For the coming week, the amounts of the three main ingredients the company has in storage are as follows:

Ingredient  Availability 
Starch 150 lbs
Sugar 130 lbs
Fruit juice 15 gallons

The Ortaköy and Beyoglu flavors use the following amounts of the main ingredients (per box):

Flavor   Starch (lbs) Sugar (lbs) Fruit juice (gallons)
O 0.1 0.05 0.03
B 0.3 0.1 0.02

The company needs to decide how many boxes of each flavor to make during the coming week to maximize its weekly profit without exceeding the availabilities of the ingredients or the size of the Turkish delight market.

Let NO be a decision variable that expresses the number of boxes of the Ortaköy flavor to make during the coming week, and let NB be a decision variable that expresses the number of boxes of the Beyoglu flavor to make during the coming week.

Suppose that ZI decides to make 250 boxes of Ortaköy and 350 boxes of Beyoglu. What is the weekly profit that it will earn? 

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ISBN:
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Cengage,