Standard deviations of the four activities of the critical path are 1,2,4,2.
Standard deviation of this critical path = Sum of square root of variance of this corresponding critical path
Standard deviation of critical path
Now we need to find the probability that the project will completed in 38 weeks given that its expected completion time is 40 weeks.
That is, we need to find P(X<38) :
Probability
Thus the probability that the project will be completed in 38 weeks is 0.34.
We have been given a system of inequalities and an objective function.
The inequalities are given as:
And the objective function is given as:
In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.
The graph of the region is shown below:
From the graph, we can see that corner points of the feasible region are:
(x,y) = (15,30),(30,15) and (30,60).
Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.
Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30
