Suppose that an individual has an income of $400 all of which he/she spends on two goods Y and X. If he/she spends all of his/her income on Y, the maximum amount of Y he/she can consume is 100 units. If he/she spends all of his/her income on X, the maximum amount of X he/she can consume is 50 units. Suppose further that, given the amount of time the individual has available, he/she can consume no more than 80 units of Y if he/she consumes all Y and 70 units of X if he /she consumes all X.
Draw a budget line for the individual and show where he/she will maximize utility assuming that both income and time are binding constraints on his/her behavior.