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Problem 1: Consider the following linear program in which we wish to determine the number of toy soldiers (x1) and toy trains (x2) to produce to maximize profit subject to limitations on finishing labor, carpentry labor, and demand for toy soldiers: max s.t. +x2 0 (hours of finishing labor) (hours of carpentry labor) (demand for toy soldiers) After adding slack variables, the optimal tableau is as follows: Z 1 0 0 0 X1 0 1 0 0 X 0 0 1 0 S1 1 1 -1 -1 S2 1 -1 2 1 S3 0 0 0 1 RHS 180 20 60 20 Use this tableau to answer the following questions. Part a: Show that as long as soldiers (xl) contribute between $2 and $4 to profit, the current basis remains optimal. If soldiers contribute $3.50 to profit, find the new optimal solution. Part b: Show that as long as trains (xz) contribute between $1.50 and $3.00 to profit, the current basis remains optimal. Part c: Show that if between 80 and 120 finishing hours are available, the current basis remains optimal. Find the new optimal solution if 90 finishing hours are available. Part d: Show that as long as demand for soldiers is at least 20, the current basis remains optimal. Part e: What is the shadow price for the "carpentry labor" constraint