Final answer:
The demand for hamburgers is affected inversely by the price of a complement like cheese and potentially positively by the price increase of a substitute like hot dogs. The overall impact on hamburger demand when both a complement's and a substitute's prices increase is uncertain without more information.
Step-by-step explanation:
The student has inquired about the relationship between the price of hamburgers and the quantity demanded when cheese, a complement, varies in price. According to economic principles, when the price of a complement like cheese increases, the demand for the related good, in this case, hamburgers, would tend to decrease because the two are typically consumed together. Conversely, if the price of a substitute like hot dogs increases, the demand for hamburgers might increase as consumers switch to the less expensive option. However, if both a substitute's price and a complement's price rise at the same time, it's unclear how this will affect the demand for hamburgers without additional information about consumer preferences, the degree of the price changes, and other market factors. A graph illustrating the shifts in demand with respective price changes can be helpful for visualizing this.