Minerva Manufacturing produces three products, Platinum, Silver and Gold, each of which must be processed in Department A, Department B, and Department C. Customers demand ten units of Platinum, eleven units of Silver, and nine units of Gold per day. Each of the three departments employs five workers, who each work eight hours per day. The only constraint in each department is labor time. Each unit of Platinum requires two hours of processing in Department A, two hours and 42 minutes of processing in Department B, and 24 minutes of processing in Department C. Each unit of Silver requires an hour of processing in both Department A and Department B, and three hours of processing in Department C. Each unit of Gold requires two hours of processing in both Department A and Department C, and one hour of processing in Department B. Each unit of Platinum sells for $6,000 and requires $1,000 in direct materials. Each unit of Silver sells for $570, and requires $120 in direct materials. Each unit of Gold sells for $600 and requires $240 in direct materials. Determine the optimum product mix given current production constraints.