Problem 4 (14 marks in total). You are given the following linear programming problem.

(a) Based on the information provided in the first report, what is the total cost optimal cost? (Show your calculation, if any.) (b) What would be the effect on the total cost if the minimum particulates reduction level increased by one pound? (c) What is the validity range for the shadow price associated with the second constraint (Minimum sulfur oxides reduction)? (Show your calculations, if any) (d) In a few words, explain why some shadow prices (6 in total) are non-zero, whereas others (3 in total) are zero.

minz=8x1+10x2+7x3+6x4+11x5+9x6 subject to : 12x1+9x2+25x3+20x4+17x5+13x66035x1+42x2+18x3+31x4+56x5+49x615037x1+53x2+28x3+24x4+29x5+20x6125xj1,forj=1,2,,6xj0,forj=1,2,,6(Minimunparticulatereduction)(Minimunsulfuroxidesreduction)(Minimunhydrocarbonsreduction) Remark: The objective function is a total cost, and the coefficients are in millions of dollars. The problem has been solved with a software package, and the two following reports were generated: Conctrointc