Answer each part of each question. Show your work when appropriate. Partial credit will be awarded so attempt to answer each question, but please stay on topic with your answers.

1. Commuters in a city have preferences over miles traveled by bus (B) and miles driven (D) given by

U(B, D) = B^(1/2)+ D^(1/2)

Suppose bus travel costs PB cents per mile and car travel costs PD cents per mile.

(a) Write the budget constraint for a commuter whose total travel budget is I.

(b) Write the Lagrangian equation you would use to solve for the commuter's optimal bundle.