A major shopping mall developer in Ann Arbor is selecting the tenants mix for its next facility. Stores of various product types i are being considered for arrangement into the new mall's different sectors j. Each sector will have area C (in thousands of square feet), and funds calculated using c_i (dollars per square foot) must be set aside for "finishing" of areas allocated to stores of type i. From prior experience, the developer can estimate the present worth p_ij of revenues from a type i store located in sector j, and can further estimate the required floor space a_i (in thousands of square feet) for a type i store. The developer seeks a tenants mix that will maximize total present worth while: (i) having between n_i and Ni stores of each type i; (ii) having a total area between f_i and F_i (thousands of square feet) devoted to stores of each type i; and, (iii) not exceeding a budget of b (dollars) for finishing costs. Fractional stores are permitted.

(a) Formulate a data-independent linear program for this tenant mix problem. Be sure to define your indices, sets, parameters, and decision variables clearly.

(b) Upon further review, the developer has decided that some product types should not be placed in certain sectors. Modify your model from part (a) accordingly.

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