Jaycee's department store chain is planning to open a new store. It needs to decide how to allocate the $100,000$ square feet of available floor space among seven departments. The accompanying data includes the expected performance of each department per month, in terms of square feet $($sf$).$ 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is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, and so on$.$ For instance, electronics loses $24\%$ of its total investment, furniture loses $12\%$ of its total investment,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. Assume that it is not required that the entire available floor space be used. Answer parts a and $b$ below.

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Expected Performance Data

$\backslash$table$[[$Department$,$Investment$/$sf$,\backslash$table$[[$Risk as a $\%],[$of $ invested$]],$Minimum sf$,$Maximum sf$,\backslash$table$[[$Expected Profit$],[$per sf$]]],[$Electronics$,$$$100,24,6,000,30,000,$$$13\mathrm{.}00$