National Oil Company (NATOCO)must Plan the Shutdown of Its Houston

National Oil Company (NATOCO)must plan the shutdown of its Houston refinery for routine preventive maintenance.Each hour of downtime is lost production time and is very costly,so NATOCO wants the maintenance project completed in 22 hours.The PERT network below shows the precedence relationships of the activities involved in the project.The table gives the activity times and costs under normal operations and maximum crashing.
NATOCO wants to know the minimum cost of completing the maintenance project within the 22-hour period.Formulate and solve a linear program that will yield this information. $$\begin{array} { c c c c c } \text { Activity } & \begin{array} { c } \text { Normal } \\\text { Time (hr) }\end{array} & \begin{array} { c } \text { Normal } \\\text { Cost }\end{array} & \begin{array} { c } \text { Crash } \\\text { Time (hr) }\end{array} & \begin{array} { c } \text { Crash } \\\text { Cost }\end{array} \\\text { A } & 2 & \$ 2,000 & 1.5 & \$ 3,000 \\\text { B } & 4 & 3,000 & 3 & 3,500 \\\text { C } & 1 & 1,500 & 1 & 1,500 \\\text { D } & 4 & 5,300 & 2.5 & 8,000 \\\text { E } & 6 & 5,400 & 5 & 7,000 \\\text { F } & 10 & 6,000 & 8 & 9,000 \\\text { G } & 8 & 4,800 & 5 & 9,900 \\\text { H } & 2 & 2,800 & 1 & 2,900 \\\text { I } & 5 & 4,500 & 4 & 5,000 \\\text { J } & 12 & 6,000 & 6 & 9,600 \\\text { K } & 7 & 7,000 & 4 & 9,700 \\\text { L } & 11 & 8,800 & 9 & 9,200 \\\text { M } & 4 & 1,000 & 1 & 7,000\end{array}$$