the most important thing in this question is to demonstrate that the shadow prices for both problems are equal.so that is why shadow prices are not given in the question

just do this question...I need answer of both parts

+ Question 3 [20 marks] (a) Consider two linear programming problems: Problem LPL: maximise 11 + subject to 01111 + 41212 b2 11:12 0 and Problem LP2: max itnise 1000121 + 100c222 subject to 10001121 + 10041232 Sb 100a2121 + 100a2222 by > 0 Suppose that in an optimal solution of LP1 the variables x, and r, are basic. Moreover, there exists an optimal solution of LP2, in which the variables 2 and 22 are basic. Express the optimal values of 21 and in terms of the optimal values of 11 and 12. Will both problems have the same value? Verify that the shadow prices of the constraints in LPI are respectively equal to the shadow prices of the constraints in LP2. 3 [15 marks] In order to transform a linear programming problem into a form suitable for applying the simplex method it is often required to replace a free variable by the difference of two non-negative variables. With reasons, explain whether these two variables may both be basic in some basic solution. (5 marks) I need both parts