This problem includes $2$ questions A department store chain DCA is planning to open a new store. The company has gathered $$20$ million to invest in this new store.$$ It needs to decide how to allocate the $100,000$ square feet of available floor space among seven departments in order to maximize the expected profit. Data on expected performance of each department per month, in terms of square feet $($sf$)$ are as follows: Department Investment per sf Risk per $ invested Minimum sf Maximum sf Expected profit per sf Electronics $$$$100\mathrm{.}0024\%600030000$$$12\mathrm{.}00$ Furniture $$$$50\mathrm{.}0012\%1000030000$$$6\mathrm{.}00$ Men's clothing $$$$30\mathrm{.}005\%20005000$$$2\mathrm{.}00$ Women's clothing $$$$600\mathrm{.}0010\%300040000$$$30\mathrm{.}00$ Jewelry $$$$900\mathrm{.}0014\%100010000$$$20\mathrm{.}00$ Books $$$$50\mathrm{.}002\%10005000$$$1\mathrm{.}00$ Appliances $$$$400\mathrm{.}003\%1200040000$$$13\mathrm{.}00$ The company has gathered $$20$ million to invest in floor stock. The risk column is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, and so on$.$ For instance, Electronics loses $24\%$ of its total investment, furniture loses $12\%$ of its total investment, and so on$.$ The amount of risk should be no more than $10\%$ of the total investment. Question $1$:$$ Formulate the LP problem: identify the decision variables, state the objective function and the constraints,$$ and identify any upper or lower bounds on the decision variables $$ Question $2$:$$ a$)$ Implement the linear optimization model that you developed in Question $1$ on a spreadsheet $$ b$)$ Use the solver to find an optimal solution $$ c$)$ Interpret the Solver Answer Report and identify the binding contraint$($s$)$