An orange juice containing $25\mathrm{.}0$ wt$\%$ of solids and the balance water sells for $$18\mathrm{.}00/$kg$.$ Another orange juice mixture containing $12\mathrm{.}0$ wt$\%$ solids sells for $$10/$kg$.$ If a retailer produces a $1$ kg blend containing $17\mathrm{.}0\%$ solids, $($a$)$ how much of the amount required for each juice$($b$)$ how much $($$$/$kg$)$ should it be sold for to yield a $10\%$ profit?$($c$)$ Draw the flowchart for the scaled processes if the manufacturing line to produce the blending juice is $1000$ kg$/$h$.$