Interest rate​ (with changing​ years). Keiko is looking at the following investment choices and wants to know what annual rate of return each choice produces. a.  Invest ​$360.00 and receive ​$788.17 in 11 years. b.  Invest ​$3 comma 000.00 and receive ​$11 comma 499.87 in 17 years. c.  Invest ​$31 comma 542.31 and receive ​$140 comma 000.00 in 22 years. d.  Invest ​$32 comma 895.12 and receive ​$1 comma 100 comma 000.00 in 40 years.

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.