Your job is to design a mixer to produce $200k\frac{g}{?}$ day battery acid. The batter acid must contain $18\mathrm{.}6wt\%$ sulfuric acid in water. Raw materials available include a concentrated sulfuric acid solution at $62wt\%$ acid, a dilute solution at $10\mathrm{.}8wt\%$ sulfuric acid, and waste acid solution that contains $0\mathrm{.}5wt\%$ acid. The concentration solution costs $10$ cents $\frac{?}{kg},$ the dilute solution costs $2$ cents $\frac{?}{kg},$ and the waste acid is free. Draw a flow diagram and complete a DOF analysis. Derive an equation that relates the product cost to the cost and flow rates of the raw materials. Then determine the optimum flows of the concentrated acid, dilute

acid, and water into the mixer