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This article studies optimal investment in flexible manufacturing capacity as a function of product prices (margins), investment costs and multivariate demand uncertainty. We consider a two-product firm that has the option to invest in product-dedicated resources and/or in a flexible resource that can produce either product, but has to make its investment decision before demands are observed. The flexible resource provides the firm with a hedge against demand uncertainty, but at a higher investment cost than the dedicated resources. Our analysis highlights the important role of price (margin) and cost mix differentials, which, in addition to the correlation between product demands, significantly affect the investment decision and the value of flexibility. Contrary to the intuition also prevalent in the academic literature, we show that it can be advantageous to invest in flexible resources even with perfectly positively correlated product demands.