Please answer all of this please

In return for their with optimizing his painting project, the castle servant informed poly and digit that he saw someone dressed as the king leaving behind a trail of crumbs as he walked into the jester's room late last night. poly and digit have finally found the crisp-collecting culprit — it turns out the jester's shoe size and hair color match the clues that were found! in gratitude, poly and digit agree to the servant with his current task of replacing all of the tables and chairs in the castle. his goal is to determine which furniture company should produce the new furniture. he receives information from a company that customizes elegant furniture, and he wants to analyze the company's production process in order to calculate some problems about cost and availability. read the following scenario, and assist poly and digit as they the servant with his calculations. the fit for a king furniture company requires 2020 hours of labor to produce a standard table, and a chair requires 1212 hours of labor. the labor available is 565565 hours per week. the company can produce at most 3535 chairs per week.

Grant, inc., acquired 30% of south co.’s voting stock for $200,000 on january 2, year 1, and did not elect the fair value option. the price equaled the carrying amount and the fair value of the interest purchased in south’s net assets. grant’s 30% interest in south gave grant the ability to exercise significant influence over south’s operating and financial policies. during year 1, south earned $80,000 and paid dividends of $50,000. south reported earnings of $100,000 for the 6 months ended june 30, year 2, and $200,000 for the year ended december 31, year 2. on july 1, year 2, grant sold half of its stock in south for $150,000 cash. south paid dividends of $60,000 on october 1, year 2. before income taxes, what amount should grant include in its year 1 income statement as a result of the investment?

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.