A particular individual consumes two goods, X and Y. This consumer's marginal rate of substitution of X for Y is MRSXY = 2Qy/3Qx. The consumer's current income is 750, while the prices of X and Y are 6 and 2, respectively.

a. Determine the consumer's utility-maximizing (optimal) bundle of X and Y.

b. Graph the consumer's optimization problem, with the quantity of good X on the horizontal axis and the quantity of good Y on the vertical axis. Your figure should include the consumer's budget line and any relevant indifference curve(s). Be sure to label the intercepts of the budget constraint as well as the consumer's optimal consumption bundle.

c. Graph the demand curve for good X by finding QX at prices of 4 and 10 for this good (in addition to the original price-quantity pair from part a).