Consider the same situation with 4 assets and the following expected rates of return and variance-covariance matrix: 0.1784 0.093857 -0.000233 0.000195 -0.000094 m= 0.0234 V= - 0.000233 0.051747 -0.000149 0.000081 0.1320 0.000195 -0.000149 0.056614 -0.000052 0.1375 -0.000094 0.000081 -0.000052 0.060000 1) Find the weights of a portfolio that achieves an expected rate of return of 10% with the lowest possible variance (or standard deviation). 2) Show that using the weights obtained you do indeed have a portfolio expected return of 10% (i.e., verify the result you just obtained) 3) Compute the resulting portfolio's standard deviation. How does this optimal portfolio compare against asset # 2 ?.

1. Consider the scheduling of tasks involved in building a house on a foundation that already exists.
We know how long it takes to carry out each task and which tasks must be completed before
commencing any particular task. The tasks that need to be performed in building this house, their
immediate predecessors, and an estimate of their duration are as follows: Task Immediate
Predecessors Duration 0 Start 0 1 Framing 0 2 2 Roofing 1 1 3 Siding 1 1 4 Windows 3 2.5 5
Plumbing 3 1.5 6 Electricity 2, 4 2 7 Inside Finishing 5, 6 4 8 Outside Painting 2, 4 3 9 Finish 7,
8 0 Let T_i denote the start time of the task i=0,1,..., 9. In particular, based on the above details
we know that T_0=0. Thus the total time required to execute the project is T_9. Write an
optimization model with the 10 decision variables T_0, T_1, T_2,..., T_9 to determine in what
sequence the tasks should be performed in order to minimize the total time required to execute
the project, T_9.