Now that he's retired, Ted has plans to zoom around town on a motorcycle. He has picked a Yamaha YZF-R6 that costs $14,199 and has $2000 saved up for a down payment. If he qualifies for a loan with a 5.79% APR and wants to make a monthly payment of $250, how long will it take for him to pay off his bike

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.