EconomicsLinear ProgrammingMusicStatistics and ProbabilityComputer GraphicsImage CompressionDiscrete Dynamical SystemsFractalsMath 2270-003ProjectsComplete one of the following projects, due on the last day of class. You mayuse Maple or another program of your choice. You must work independently.You may also come up with your own project or do some variation of one ofthe suggestions, but you should consult me first.1 EconomicsUse the 2008 Summary Use Annual I-O Table found at http://www.bea.gov/industry/io annual.htmto construct a consumption matrix as in Section 8.3. Was this economy pro-ductive?Related: Section 8.3[Sample Code and Data]2 Linear ProgrammingRelated: Section 8.4[Sample Code and Data]3 MusicCompare the waveforms of several musical instruments playing the same note.Compare their energy spectra.Related: Lab 4, Section 8.5, Section 7.3, Section 10.3[Sample Code and Data]4 Statistics and ProbabilityReconsider the height-weight data from Lab 3. Assume that each person un-derestimates their weight randomly by 2-4%. Use the weighted least squaresmethod of Section 8.6 to find a more accurate model function for the height-weight data. Plot the data, new model, and old model together on the same setof axes. Pick a height (it was 5’10” in Lab 3) and compute the expected weightof a person of that height using the two different models.Related: Lab 3, Section 8.6[Sample Code and Data]5 Computer GraphicsTake a 3–dimensional wireframe model and move it around using the techniquesof Section 8.7.1Related: Section 8.7[Sample Code and Data]6 Image CompressionTake a bitmap image and compress it using two different methods, using thelargest singular values of the SVD and using the largest values of the FourierTransform. Experiment with how many values you must retain to have accept-able image quality.Related: Section 6.7, Section 7.2, Section 10.3[Sample Code and Data]7 Discrete Dynamical SystemsWe have talked a lot about discrete linear dynamical systems. Compute orbitsfor some discrete linear dynamical systems in the plane. Plot orbits for systemswhere the eigenvalues are real with absolute values less than one, one, andgreater than one. Plot orbits for systems whose eigenvalues are complex withnorm less than one, one, and greater than one.Consider the non-linear discrete dynamical system that takes a point (xi, yi)in the plane and moves it to the point (xi+1, yi+1) where:xi+1= yi+ 1 − ax2iyi+1= bxiTry setting a = 1.4 and b = .3. Plot some orbits and discuss the results.What happens for different values of a and b?Related:[Sample Code and Data]8 FractalsMake some fractals. See Part B of