Sandhill Co. sells office equipment on July 31, 2022, for $22,430 cash. The office equipment originally cost $77,870 and as of January 1, 2022, had accumulated depreciation of $36,830. Depreciation for the first 7 months of 2022 is $4,580. Prepare the journal entries to (a) update depreciation to July 31, 2022, and (b) record the sale of the equipment. (Credit account titles are automatically indented when amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.)

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.