Diemans Corp. has provided a part of its budget for the 2nd quarter: Apr May Jun Cash collections $ 40 comma 000 $ 42 comma 000 $ 42 comma 000 Cash payments Purchases of inventory 4 comma 500 7 comma 000 7 comma 200 Operating expenses 7 comma 200 9 comma 000 6 comma 000 Capital expenditures 4 comma 600 20 comma 000 0 The cash balance on April 1 is $ 14 comma 000. Assume that there will be no financing transactions or costs during the quarter. Calculate the cash balance at the end of April.

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.