Penicillin is produced by Penicilhum chrysogenum in a fed-batch culture with the intermittent addition of glucose solution to the culture medium. The initial culture volume at quasi-steady state is V0 = 500 I. and glucose-containing nutrient solution is added with a flow rate of F = 50 Ilh. Glucose concentration in the feed solution and initial cell concentration are S ₀ = 300 g/I and X3 = 20 g/I. respectively. The kinetic and yield coefficients of the organism are μm = 0.2 h ^-1 , k _s = 0.5 g/I, and Y _X/S = 0.3 g dw/g glucose.
a. Determine the culture volume at t = 10 h.
b. Determine the concentration of glucose at t = 10 h at quasi-steady state.

c. Determine the concentration and total amount of cells at quasi-steady state when t = 10 h.

d. If q _p = 0.05 g product/g cells h and P ₀ = 0.1 g/l determine the product concentration in the vessel at t = 10 h.

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