please show all work.

Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: MaximizeZ=Subjectto:1x1+1x22x1+1x260(C1)1x1+2x260(C2)X1,x20 The optimum solution is: x1=20.00(roundyourresponsetotwodecimalplaces).x2=20.00(roundyourresponsetotwodecimalplaces). Optimal solution value Z=40.00 (round your response to two decimal places). If a technical breakthrough occurred that raised the profit per unit of X1 to $3, due to this change, the optimal solution As a result of the technical breakthrough, the optimum solution is: X1=30.00 (round your response to two decimal places). X2=0.00 '(round your response to two decimal places). Optimal solution value Z=90.00 (round your response to two decimal places). If the impact of technical breakthrough was incorrectly determined and instead of X1 profit coefficient increasing to $3 it only increases to $1.25. As a result of this correction, the optimal solution found originally