This problem is concerned with one of the simplest types of linear programs in which there is a single linear constraint and there are lower and upper bounds on variables: a) (5 points) For every value b with 0 b 10, F(b) denotes the following problem: maximize 6x +4x2+2x3 + x4 subject to 1+X2+X3+x4 b 0x 2, 0 x2 3, 0 x3 1, 0 x4 4 i) (3 points) Code the LP using Gurobi, and solve it for b = [0, 10] (= {0, 1, 2, 3, ..., 10}). (Remember to upload every code you write with your problem set.) ii) (2 points) Let (.) be the optimal value function. That is, f(b) is the optimal value when the right-hand side is b. Graph f(b) for 0 b 10 using Python or Excel. Hint: use a Scatter Plot with Straight Lines and Markers