A new shopping mall is being built, and management is determining which stores the mall should...

 

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A new shopping mall is being built, and management is determining which stores the mall should include. The total amount of space available for the mall is 55000 square feet. Management has decided that no more than 25 percent of the space in the mall must be dedicated to stores that serve food and drink, at least 50 percent of the space must be dedicated to stores that sell clothes, at least 20 percent of the space dedicated to stores that sell electronics, and at least 45 percent of the space dedicated to stores primarily targeted towards teenagers and younger adults. The following stores have applied for space at the mall, each listed with their product offerings: Store Apple H&M Burberry Starbucks Panera Bread American Eagle Macy's Food/Drink Clothes Electronics No Yes Yes No No Yes Yes No No No Yes Yes No No Yes No No No No No Yes For teens Space (1000 sq ft) Bid No $2600 Yes $3200 No No No Yes No 6 12 5 3 7 11 15 $2000 $2400 $2800 $3000 $3400 The bid amount is the amount the mall will earn if the given store is chosen. For the purposes of this problem, we may select fractions of stores, such that the bid and space of the store will decrease proportionally. For example, if half of Apple is chosen, the floor space used would be 1500 square feet and the amount earned would be $1300. More than 100 percent of a store cannot be chosen. All mall space must be used. (a) Formulate a linear program that will allow the mall to decide what percentage of each shop should be chosen in order to maximize the total revenue from the stores. Provide the specific model. (b) Provide the generic model of the linear program. Make sure to define all variables and parameters clearly. A new shopping mall is being built, and management is determining which stores the mall should include. The total amount of space available for the mall is 55000 square feet. Management has decided that no more than 25 percent of the space in the mall must be dedicated to stores that serve food and drink, at least 50 percent of the space must be dedicated to stores that sell clothes, at least 20 percent of the space dedicated to stores that sell electronics, and at least 45 percent of the space dedicated to stores primarily targeted towards teenagers and younger adults. The following stores have applied for space at the mall, each listed with their product offerings: Store Apple H&M Burberry Starbucks Panera Bread American Eagle Macy's Food/Drink Clothes Electronics No Yes Yes No No Yes Yes No No No Yes Yes No No Yes No No No No No Yes For teens Space (1000 sq ft) Bid No $2600 Yes $3200 No No No Yes No 6 12 5 3 7 11 15 $2000 $2400 $2800 $3000 $3400 The bid amount is the amount the mall will earn if the given store is chosen. For the purposes of this problem, we may select fractions of stores, such that the bid and space of the store will decrease proportionally. For example, if half of Apple is chosen, the floor space used would be 1500 square feet and the amount earned would be $1300. More than 100 percent of a store cannot be chosen. All mall space must be used. (a) Formulate a linear program that will allow the mall to decide what percentage of each shop should be chosen in order to maximize the total revenue from the stores. Provide the specific model. (b) Provide the generic model of the linear program. Make sure to define all variables and parameters clearly.

Answer rating: 100% (QA)

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