Excel's Solver to find the critical path duration (without crashing):
The objective is set to a minimum in the dialog box on the right, and the various constraints regarding the formulated LP is added. As can be seen from the figure below (cell D2), the optimal duration is 6.4 min for the critical path.
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Excel's Solver to find the minimum cost to finish the critical path in a faster time (with crashing):
The objective is set to a minimum in the dialog box on the right, and the various constraints regarding the newly formulated LP (with crashing) is added. The desired time for the jobs to be completed is 5 min (as indicated in F4). As can be seen from the figure below (cell F3), the minimum cost is R104.50 for the minimized duration.