d) The final simplex table for the above problem is given below. Note: s1, s2and s3 relates to preparation cost, man-days of work and land area respectively. Basic Quantity 30 40 20 0 0 Variables X1 X2 X3 S1 S2 S3 X1 250 -1.625 0.0625 -0.75 0 X2 625 0 1.9375 - 0.625 0.0438 S3 125 0 0.6875 - 0.125 1 0.0188 Zj 32500 30 40 28.75 0.125 2.5 0 Cj -Zj 0 0 -875 -0.125 -2.5 0 As per the above table; (i) What is the optimal solution? (2 marks) (ii) Interpret the shadow prices of preparation cost and man-days of work. (2 marks) (iii) Construct the dual for the problem. (iii) Construct the dual for the problem. (5 marks) (iv) Find the optimal values for the dual variables. (2 marks) (v) Find the range within which the production of corn can be changed without affecting the optimal solution. (3 marks) (vi) Find the range within which the production of millet can be changed without affecting the optimal solution. (3 marks) (vii) Find the range within which the production of cowpie can be changed without affecting the optimal solution. (3 marks) (viii) Identify the range within which preparation cost can be varied without altering the optimal solution. (3 marks) (ix) Identify the range within which man-days of work can be varied without altering the optimal solution