(eng): An optimal control problem governed by a linear elliptic equation with a control acting as a coefficient matrix is considered. This matrix is symmetric, uniformly positive definite, can be large but may vary only in a single prescribed direction. Using a homogenization theory for posibly stiff stratified media, a relaxation theory is developed and, in a special case, differentiability of the extended cost functional is proved and a point-wise maximum principle necessary for an optimal composite is derived.