Question: Problem 4 ( 14 marks in total). You are given the following linear programming problem. min28x1+10x2+7x1+6x4+11x1+9x6 subject to: 12x1+9x2+25x1+20x1+17x2+13x260 (Minimun particulate redaction) 35x1+42x2+18x1+31x4+56x2+49x2150 (Minimun sulfur

Problem 4 ( 14 marks in total). You are given the

Problem 4 ( 14 marks in total). You are given the following linear programming problem. min28x1+10x2+7x1+6x4+11x1+9x6 subject to: 12x1+9x2+25x1+20x1+17x2+13x260 (Minimun particulate redaction) 35x1+42x2+18x1+31x4+56x2+49x2150 (Minimun sulfur axides reduction) 37x1+53x2+28x1+24x4+29x1+20xk125 (Minimin lyydrocarbons reduction) xj1, for j=1,2,,6 x,0, for j=1,2,,6 Remark: The objective function is a total cost, and the cecfficients are in millions of dollars. The problem has been solved with a soffware package, and the two following reports were generated: (a) (5 manks) Based on the information provided in the first report, what is the total cost optimal cost? (Show your calculation, if any.) (b) (3 marks) What would be the effect on the total cost if the minimum particulates reduction level inereased by one pound? (c) (3 manky) What is the validity range for the shodow price associated with the second constraint (Minimum salfur oxides reduction)? (Show your calculations, if any) (d) 3 manks) In a few words, explain why some shadow prices (6 in total) are non-zero, whereas others ( 3 in total) are zero

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