A batch process requires the following operations to be completed in sequence: \(3 \mathrm{hr}\) of mixing, \(5 \mathrm{hr}\) of heating, \(4 \mathrm{hr}\) of reaction, \(7 \mathrm{hr}\) of purification, and \(2 \mathrm{hr}\) of transfer.

(a) When the five operations are carried out in vessels U1, U2, U3, U4, and U5, respectively, determine the cycle times, and construct Gantt charts corresponding to the zero-wait, intermediate storage, and unlimited intermediate storage inventory strategies.

(b) When a new purification vessel U4A is purchased so that two 7-hr purifications can take place in parallel, determine the system bottleneck using the intermediate storage inventory strategy.