bv_cvxbook_extra_exercises

You must select the pipe radii rj to minimize the

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Unformatted text preview: form (−1, 1, 2, 0, . . . , 0). Reactions are also used to model flow of metabolites into and out of the cell. For example, suppose that reaction R2 corresponds to the flow of metabolite M1 into the cell, with v2 giving the flow rate. This corresponds to a second column of S of the form (1, 0, . . . , 0). 147 The last reaction, Rn , corresponds to biomass creation, or cell growth, so the reaction rate vn is the cell growth rate. The last column of S gives the amounts of metabolites used or created per unit of cell growth rate. Since our reactions include metabolites entering or leaving the cell, as well as those converted to biomass within the cell, we have conservation of the metabolites, which can be expressed as Sv = 0. In addition, we are given upper limits on some of the reaction rates, which we express as max = ∞ if no upper limit on reaction rate j is known. The goal is to v v max , where we set vj find the maximum possible cell growth rate (i.e., largest possible value of vn ) consistent with the constraints Sv = 0, v 0, v v max . The questions be...
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