The young student Ali inherits 6000 TL and has to decide between becoming partner in two different entrepreneurial ventures started by his friends Büşra and Candan. He has 600 hours to spare and is planning to join in one or both friends' ventures in whichever combination would maximize his total estimated profit. Becoming full partner in Büşra's venture requires an investment of 4000 TL and 300 hours, and the estimated profit is 4900 TL. Investing in Candan's venture requires 3000 TL and 400 hours, with an estimated return of 4900 TL. ALi can choose to enter at any fraction of a full partnership, and his share of the profit would be proportional to this fraction. Recall that Xi and X2 are the fractional investment in Büşra's and Candan's ventures respectively. You helped Ali formulate the problem of finding the best combination. The initial and final tableaux are given below: 

Initial Tableaux: 

a) Construct a dual problem from initial Tableaux. 

b) What is the maximum allowable change in the returns from either venture fort he current solution to remain optimal? (Hint: Sensitivity for C and C2)

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Basic Coeff Var RHS X2 X3 -4900 -4900 XI X4 1 4000 3000 1 6000 300 400 600 Final Tableaux: Basic Coeff Var XI X3 X4 RHS 8400 1/7 1/7 7/10 -4/700 3/700 3/700 -4/700 4/700 -3/700 -3/700 4/700 6/7 6/7 3 00- 100 RO-OOO ao- O00 OO 010 N-OO OO Basic Coeff Var RHS X2 X3 -4900 -4900 XI X4 1 4000 3000 1 6000 300 400 600 Final Tableaux: Basic Coeff Var XI X3 X4 RHS 8400 1/7 1/7 7/10 -4/700 3/700 3/700 -4/700 4/700 -3/700 -3/700 4/700 6/7 6/7 3 00- 100 RO-OOO ao- O00 OO 010 N-OO OO