We develop a general method for solving screening problems with multi-dimensional types and one-dimensional `physical' allocation space.

Our method is based on characterizing and computing the isoquants, the sets of types who are allocated the same quantity (or quality) of the good, and then assigning the quantities optimally along the boundary of the set of types who get positive quantities in the optimal mechanism.

The optimal mechanism exhibits a number of qualitative properties that distinguish this setting from the one dimensional case. In particular, the optimal allocation exhibits discontinuity along the boundary of the region of excluded types.

We illustrate the application of our method to an example with uniformly distributed types.