A specific 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.
Determine the consumer's utility-maximizing (optimal) bundle of X and Y.
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 to show the optimal consumption bundle (The indifference curve does not need to have a specific shape, just the properties required of the indifference curve through the optimal point). Be sure to label the intercepts of the budget line, the slope of the budget line, as well as the consumer's optimal consumption bundle.