Question: a) Alphonse travels for work, and can choose either to fly or drive. While he prefers to fly, any money he saves on airfare can be spent on fancier dinners at his destination. Alphonse's utility function is \(U\left( F,M \right)=8{{F}^{3/2}}{{D}^{1/2}}\) , where F and D are number of flights and dinners, respectively. His travel budget is $1,000. The price of a flight is PF=$200, and the price of a meal is PD=$50. What is his utility maximizing combination of flights and meals?

b) The airline offers Alphonse a VIP card, which will allow him to purchase tickets for $150, rather than $200. If Alphonse buys the card, what is his new optimal bundle of flights and dinners?

c) At most, how much would Alphonse be willing to pay for this card? (i.e., what is the size of the compensating variation?)