Yes, the corner solution is best because his MRS is less than the price ratio.
Bill uses his entire budget to purchase Pepsi and hamburgers, and he currently purchases no Pepsi and 6 hamburgers per week. The price of Pepsi is $1 per can, the price of a hamburger is $2, Bill's marginal utility from Pepsi is 2, and his marginal utility from hamburgers is 6. Is Bill's current consumption decision optimal? T/F