For a certain alcohol-free party, you are responsible for

buying 10 dozens a certain brand of soda and there are many, many shops selling

that soda. We know for sure that the price per dozen at a

shop is equally likely to be anywhere between $8 and $16. The time and other costs for

you to visit one shop are $5. You want to search for the lowest price but you do not want

to waste too many resources looking around.

a) By equating the marginal benefit and marginal cost of visiting another shop, solve for

the optimal number of shops to visit (use the smaller round number).

b) How does your answer in a) change when you are buying 20 dozens instead?

c) How does your answer in a) change when the price is uniformly distributed between

$6 and $12 instead?