Implement the \pqr product mix" problem discussed in class (see below) using python and gurobi with its rhs parameterized by . we are interested in understanding the impact of increasing the machine availabilities on the optimal cost. the \rates" at which we can increase the availability of the four machines are respectively, 3, 2, 1, 0, as represented by 1 the coecient of the parameter in the rhs of the constraints. develop a plot of the optimal pro t as a function of ; what do you observe from the plot regarding the function z() = max 45x1 + 60x2 + 50x3 subject to: 20x1 + 10x2 + 10x3 2400 + 3 12x1 + 28x2 + 16x3 2400 + 2 15x1 + 6x2 + 16x3 2400 + 10x1 + 15x2 + 0x3 2400 x1 100 x2 40 x3 60 x1 0 x2 0 x3 0