You, a consumer, live in a world with two goods, x and y. Your utility function over bundles of the goods is u(qx, qy ) = min{qx 2qy , 2qx qy } I.e., your utility is either qx 2qy or 2qx qy , whichever is smaller. (a) What is your utility from the bundle (8, 2)? (b) In a graph, draw the line that shows all bundles such that qx 2qy = 12. (c) In the same graph, draw the line that shows all bundles such that 2qx qy = 12. (d) What is the one bundle (qx, qy ) such that qx 2qy = 12 and 2qx qy = 12 are both true? Find it using algebra. (e) In a new graph, graph the indifference curve through bundle (8, 2). Hint: it will have something (a lot) to do with your answers to (b), (c), and (d). (f) What is your marginal rate of substitution at the bundle (8, 2)? Hint: if your indif- ference curve was straight at (8, 2), you could find the marginal rate of substitution at (8, 2) by finding the slope of the indifference curve at (8, 2)