Problem \# 3 (Graphical approach and sensitivity analysis, J. \& B., 2.3, pg 52, modified, [/30]) Consider the following linear optimization model mins.t.2x1+(1+)x2x1+2x210x12x24x1+x28x1+2x220x10x20 where and are parameters (i.e., they are not variables.) 1. Assume that =0 and =0. Graph the feasible region using a two-dimensional graph. Identify the lines on the graph with the constraint numbers assigned in the model. Show three isovalue contours of the objective function and indicate the direction of decrease. Identify the optimal solution on the graph. 2. Assume that =0. (a) Explain in words how the figure you drew in Part 1 would change if we set =1. (b) For all values of 0, find an optimal solution to the problem. (Hint: the values of x1 and x2 will be a function of . Consider the case 6 and 6 separately). 3. Assume that =0. (a) Explain in words how the figure you drew in Part 1 would change if we set =1. (b) For all values of (positive and negative), find an optimal solution to the problem. (Hint: there will be three main range of values to consider for .)