Its more economics problem but still. Any suggestions, tips for approach?

Many Thanks,

Charlie consumes only apples (

a) and bananas (b) every day. He maximizes the following

function:

U

(a,b) = a^(1\2) + 4 b^(1\2) .

a) Knowing that a banana is twice as expensive as an apple, find Charlie’s optimal daily

consumption as a function of his daily income m and price of banana p. (Assume that apples and bananas can be consumed not only in integer amounts.)

b) Solve the same problem if Charlie’s doctor tells him that he must consume at least

one apple every day.