Vandalay Industries sells gift cards redeemable for Vandalay products either in-store or online. During 2021, Vandalay sold $2,000,000 of gift cards, and $1,800,000 of the gift cards were redeemed for products. As of December 31, 2021, $150,000 of the remaining gift cards had passed the date at which Vandalay concludes that the cards will never be redeemed. How much gift card revenue should Vandalay recognize in 2021

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.