You private coffee shop is expecting significant growth since Amazon announced their new office site within 1 block of your store. You forecasted that your 3.4 hour breakfast time will have a demand for 796 cups of espresso. There are 3 equal sized steps of 37.2 seconds for you to make one cup of espresso. What is the minimum number of espresso machines you must have to service this demand during these [hr] hour time slot

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.