Suppose David's utility function is U(A,B) = 10AB. The price of good A is $3 and price of good B is $5. David has an income of $150.

a. What is David's optimal consumption bundle?

b. Suppose the price of good A increases to $6. How much income does David need to be able to purchase the original consumption bundle?

c. At the new price of $6 for good A, how much income is needed for the consumer to reach the original level of utility?