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In this paper, we consider optimal scheduling algorithms for scientific workows with two typical structures, fork&join and tree, on a set of provisioned (virtual) machines under budget and deadline constraints in cloud computing. First, given a total budget B, by leveraging a bi-step dynamic programming technique, we propose optimal algorithms in pseudo-polynomial time for both workows with minimum scheduling length as a goal. Our algorithms are efficient if the total budget B is polynomially bounded by the number of jobs in respective workows, which is usually the common case in practice. Second, we consider the dual of this optimization problem to minimize the cost when the deadline of the computation D is fixed. We change this problem into the standard multiple-choice knapsack problem via a parallel transformation.