I've been trying this problem for a few hours and still don't know where I'm going wrong:

Question

Consider a rational consumer with a utility function given by U(x,m)=Aln(2x)+m. The consumer needs to decide how much of good x to buy given the following pricing rule: the first 10 units sell at a price of $2 per unit; additional units sell at a price of $3 per unit.

QUESTION. What is the maximum value of A at which the consumer buys 10 units or less?