$7\mathrm{.}1$ Consider an inventory problem for three types of items. All the needed information is presented in the table below. The maximum area is $7500f{t}^2$ and the maximum total budget is $$15,000.$ Use optimization to find the optimal order quantity for each item. Also find the total cost.

$\backslash$table$[[$Item$,i,D_i($per year$),C_{R,i}($$$),C_{H,i}($$$),a_i(f{t}^2),c_i($$$),Q_{i,\text{m}\text{i}\text{n}},Q_{i,\text{m}\text{a}\text{x}}$