Major shopping mall developer Homart17 is selecting the tenant mix for its next facility.

Stores of product types i = 1,c, 20 are being considered for arrangement into the new mall’s sectors j = 1,c, 5. Each sector will have 150 thousand square feet, and an allowance of ci per square foot will be set aside for finishing of areas allocated to stores of type i. From prior experience, Homart can estimate the present worth pi, j of revenues from a type i store located in sector j and the required floor space ai (in thousands of square feet). They seek a tenant mix that will maximize total present worth while having between ni and nQ i stores of each type i totaling between fi and fQ i thousand square feet, and not exceeding the budget b for finishing allowances.

Formulate an LP model of this tenant mix problem using the decision variable xi, j ! number of stores of type i included in sector j