A firm has 56 units of product X on hand. Forecasts of demand are for 20 units per week. An MPS quantity of 100 units is planned to arrive in period 3. Customer orders are 24 for period 1, 18 for period 2, and 15 for period 3. What quantity is available for commitment to new customers prior to the receipt of the MPS quantity in week 3

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.