Suppose Sam's preferences for snack sized bags of Fritos and Doritos can be represented by the following utility function: U(F,C) = 10(FD) ? where F = the number of bags of Fritos and D = the number of bags of Doritos in the bundle. Further suppose the price of a bag of Fritos is $2.50 and the price of a bag of Doritos is also $2.50. Sam has $10 to spend on these snacks. a. Draw Sam's budget line for Fritos and Doritos, placing Fritos on the horizontal axis. Label fully, including intercepts and slope. b. Consider the following commodity bundles: W: (2, 8) X: (4, 4) Y: (2, 2) Z: (3, 3) Without using the utility function, what can we say about a rational consumer's preference ranking over these bundles? (Make all standard assumptions and rank as fully as you can given those assumptions.) c. Now consider Sam's specific preferences as represented by the utility function above. Use the utility function to rank the bundles listed in part b. for Sam. Use preference ranking notation to summarize your results. d. Suppose that Sam's optimal bundle is bundle Y. Draw a standard indifference curve map to illustrate this. Make sure the indifference curve map is also consistent with the results from parts a-c. Be sure to plot and label each bundle and each curve. e. Suppose the slope of Sam's indifference curve at bundle Y is equal to the slope of Sam's indifference curve at bundles X and Z. i. What is the slope? ii. Given these prices, would it be possible for bundles X and Z to be optimal if Sam had a larger budget? What about bundle W