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Q_m(t) =  \int_0^t q_m(t) \, dt
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B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v}
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B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v}

where

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\gamma_n = c_{t,n} \cdot V_{\phi, n} = (c_r + s_(w,n) \, c_w + s_{o,n} \, c_o + s_{g,n} \, c_g) \cdot  \phi_n \cdot V_n
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s_(w,n) + s_{o,n} + s_{g,n} = 1


The objective function is:

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