please solve question 3.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Question 3 (25%) Consider the following tableau for a profit maximization problem where X1, X2, and X3 are the number of products to be manufactured and Si and S2 are slack variables associated with the first and second resources respectively. The objective function is z = 25X, +30X+20X,. Basic X1 X3 X2 1/3 X2 1 0 0 2/3 4/3 -5 S1 1/3 -1/3 10 S2 0 1 0 RHS 40/3 95/3 400 S2 z 5/3 -10 (a) What are the optimal solution and optimal objective value according to the above simplex tableau? (4 marks) (b) How many units of the first resource are required to produce 1 unit of X2? (2 marks) (c) Determine the range of optimality for the contribution rate of X1, X2 and X3. (6 marks) (d) Determine the original values for the first and second resource. (3 marks) (e) What are the dual prices for the first and second resource? State the corresponding range of feasibility for each dual price. (6 marks) (f) How much are you willing to pay for an additional unit of the second resource? (2 marks) (g) If 5 units of the first resource were taken away, what would be the new objective function value? (2 marks)