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?

Jessica wants to plan where she will place furniture in her room, so she has drawn a scale model of her room in order to begin planning. the scale model is 11 inches long and 8.5 inches wide. jessica notices that the door to her room takes up 1.75 inches on the right-side wall of her room, and she realizes that she cannot place any furniture in the area that the door turns through when it is opened.