Graph Theory Minimal path assignment A product must be groun

Graph Theory: Minimal path assignment.

A product must be ground, polished, weighed and inspected. The grinding must precede the polishing and the weighting and the polishing must precede the inspection. Grinding takes 7 units of time, polishing takes 10 units of time, weighting takes 1 unit of time for an unpolished product and 3 units of time for a polished one, and inspection takes 2 units of time for an unweighed product and 3 units of time for a weighed one. What is the fastest production schedule?

Solution

A product must be ground, polished, weighed and inspected. The grinding must precede the polishing and the weighting and the polishing must precede the inspection. Grinding takes 7 units of time, polishing takes 10 units of time, weighting takes 1 unit of time for an unpolished product and 3 units of time for a polished one, and inspection takes 2 units of time for an unweighed product and 3 units of time for a weighed one. What is the fastest production schedule?