A developer of large shopping malls uses an optimization model to decide how many stores of each type, size and location class to include in a mall. The developer has sets I of types, J of sizes, and K of location classes to work with. The decision variables are xijk= number of stores of type i, size j and location class k, for all iI,jJ, and kK You may assume for purposes of this problem that all constraints are linear and involve just these variables. Use common algebraic notation (like " j=1naijxj " and "for all sS ") in your answers. a: The developer specifies that there may be at most Mi tenants of each type iI. Write out a linear constraint that expresses this restriction. b: A store of type i and size j requires a floor space of Aij in the mall, but there are only Gk square feet of space available for each location class kK. What linear constraints does this statement imply? c: To promote variety, the developer also wants the fruction of total floor space devoted to location class k to be at most Fk. Write a linear formulation for this constraint. d: The developer gives a "finishing allowance" of L,dollarspersquarefootto each tenant of type iI. Write out a linear constraint saying that the total of all finishing allowances must not exceed a fixed budget equal to B dollars