What is their profit per unit if they are operating at the profit maximizing output?

Anewspaper boy is trying to perfect his business in order to maximize the money he can save for a new car. daily paper sales are normally distributed, with a mean of 100 and standard deviation of 10. he sells papers for $0.50 and pays $0.30 for them. unsold papers are trashed with no salvage value. how many papers should he order each day and what % of the time will he experience a stockout? are there any drawbacks to the order size proposed and how could the boy address such issues?

Dan wants to start a supermarket in his hometown, and wants to get into the business only after finding out about the market and how successful his business might be. the best way for dan to gain knowledge is to:

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.