Christopher likes cupcakes (C) and muffins (M). His preferences can be represented by the utility function U(C, M) = C0.5M0.5. He received a gift basket with 16 cupcakes and 4 muffins, but when he was about to eat them, he found out his younger brother Dan had eaten 14 cupcakes and 2 muffins. Christopher made Dan buy what he'd eaten back. However, the bakery was out of muffins and Dan only bought cupcakes. How many cupcakes did Dan buy if, in addition to what he had not eaten from the basket, the new cupcakes provide Christopher with the same level of utility as the original gift basket?

Costco wholesale corporation operates membership warehouses selling food, appliances, consumer electronics, apparel and other household goods at 471 locations across the u.s. as well as in canada, mexico and puerto rico. as of its fiscal year-end 2005, costco had approximately 21.2 million members. selected fiscal-year information from the company's balance sheets follows. ($ millions). selected balance sheet data 2005 2004 merchandise inventories $4,015 $3,644 deferred membership income (liability) 501 454 (a) during fiscal 2005, costco collected $1,120 cash for membership fees. use the financial statement effectstemplate to record the cash collected for membership fees. (b) in 2005, costco recorded $46,347 million in merchandise costs (that is, cost of goods sold). record thistransaction in the financial statement effects template. (c) determine the value of merchandise that costco purchased during fiscal-year 2005. use the financial statementeffects template to record these merchandise purchases. assume all of costco's purchases are on credit.