U Merchandise Corp. is planning to locate a store in a new shopping center being built in fast growing section of town. The project manager assigned to the project wants to establish some guidelines for the architect who will attempt to design a building layout to fit the companyâ??s specific needs. The guidelines are to include the total number of square feet the store should contain overall, and how many square feet should be custom tailored to the requirements of each of the storeâ??s three major departments: Grocery, Clothing and Jewelry (assume there are no other departments). The architect has indicated that construction of the clothing space will cost $100 per square foot, jewelry space $300 per square foot, and grocery space $200 per square foot.
Since clothing will be the new storeâ??s merchandising specialty, the manager wants to make certain that the clothing department gets at least twice as much floor space as the other two departments combined. To maintain diversity, however, he wants each of the other departments to get at least 10 percent of the total store floor space. Total construction costs for the new store must be no more than $1 million. Past records indicate that profit contribution per square foot per day are $.75 for clothing departments, $.6 for jewelry departments, and $.80 for grocery departments.
Answer the following questions based on a linear programming formulation to determine how many square feet should be devoted to each department to maximize revenues. (Note: Xc = square feet devoted to clothing, Xj to jewelry, and Xg to grocery).
This case determines how many square feet should be devoted to each department to maximize revenues.