Do a principal component analysis of the sample data m = 1, 5, 7, 9, 4, 11, 13, 5, 4 and i = 4, 11, 12, 24, 7, 22, 29, 12, 7, where m represents the number of murders in a city for a given year and i represents the number of ice cream cones (in thousands) sold in that city for that same year. show work as appropriate (but feel free to use software to run the computations for you). if you use technology, share, interpret, and explain the output.

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.