An assembly line is being designed for manufacturing a discrete part. There are 7 operations numbered 1 to 7 to be performed on each part. Each operation can be started on a part any time after all its immediate predecessor operations given in the following table are completed, but not before. The table also gives the time it takes an operator to carry out each operation, in seconds. The cycle time of the assembly line will be 20 seconds (i.e., each operator will have up to 20 seconds to work on a part before it has to be put back on the line). An operator on the assembly line can be assigned to carry out any subset of operations, as long as the work can be completed within the cycle time and the assignments do not violate the precedence constraints among the operations. It is required to determine the assignments of operations to operators on this line, so as to minimize the number of operators needed. Formulate this as an integer program. 

Assume that we know that at most 4 operators are needed to complete the operations.

Operation Immediate predecessors Time in seconds 1 7 9. 3 1, 2 6. 4 1 4 5 3 8 6. 4 7 7 5, 6