Simple linear programming optimality models predict that utilizing a single sugar is optimal; more complex models can allow co-utilization of both sugars. a) Simplified linear programming model: The growth rate increases with the expression of the two sugar systems, E1 and E2 – dashed contours. Given a cost constraint of total proteins (blue line), expressing only one of the two sugar systems maximizes the growth rate (red dot). As the concentration of that sugar decreases, growth rate contours shift their slope, until a point in time is reached when b) the optimal solution jumps to expressing the other sugar system exclusively (yellow dot). c) If the constraint (blue line) is convex, the constraint curve bulges outwards and co-expression of the two sugar systems can be optimal (green dot). This predicts that growth rate in co-expression exceeds the maximal growth rate expressing each system alone. d) Co-expression can also be optimal if tasks other than immediate rapid growth affect fitness, for example future growth on the poorer sugar. The green box symbolizes a potential best compromise solution.