please explain and show work, thank you!

1. How many shops to visit? For a certain alcohol-free party you are responsible for buying 10 dozens of a certain brand of soda and there are many, many shops selling that soda. Before you do any search, you 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 is $5. You want to search for the lowest price but you do not want to waste too much 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