Suppose that a consumer enjoys two goods: fries and burgers. This consumer's preferences are captured by the following utility function:

U(F,B)=20F0.3B0.7 where F is the quantity of fries and B is the quantity of burgers enjoyed by the consumer.

Further, suppose that the price of a bag of fries is $3, the price of a burger is $6 and the consumer's budget is $100.

part-a: Given these numbers, find the utility maximizing consumption bundle of this consumer. Illustrate the consumer's utility maximization problem using the budget line and the indifference curves given by the Cobb Douglas type utility function in the question.

part-b: Now suppose that the price of a bag of fries increases to $4.5. Find the new utility maximizing consumption bundle and illustrate the new tangency point between the consumer's new budget line and indifference curves.

part-c: Now go back to part-a of the question and assume that the price of a bag of burgers increases to $8. Again, find the new utility maximizing consumption bundle and illustrate the new tangency point between the consumer's new budget line and indifference curves.

part-d: Again go back to part-a of the question. Now assume that the budget of the consumer increases to $120. Find the new utility maximizing consumption bundle and illustrate the new tangency point between the consumer's new budget line and indifference curves.