Elasticity of demand measures the responsiveness of quantity demanded to a change in the price of the good.
a. Perfectly elastic - The good is perfectly elastic when the consumer is ready to buy any quantity at a fixed price.
b. Perfectly inelastic- The good is perfectly inelastic when the change in the price of the good has not effect on its demand, that is when quantity demanded is same at whatever price.
So, because here Gus is ready to buy any units of cupcakes at a fixed price of $10, the demand for cupcakes should be perfectly elastic.