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For the following questions, consider the linear program given below:             

           Maximize 5(X1) + 8(X2)      

           Subject to:      

           6 (X1) + 5(X2) <= 30

           9(X1) + 4(X2) <= 36 

           1(X1) + 2(X2) <= 10 

(a) Find the optimal solution to the linear program per relaxation (in other words, assume all variables can take on any numerical value). Report the values of each variable and the optimal objective value.                 

(b) Find the optimal solution to the linear program assuming variables take on INTEGER values. Report the values of each variable and the optimal objective value.                       

(c ) Are the optimal values from part (a) and part (b) the same? If so, explain why. If not, provide explanation as to why the two LP’s produce different results. Your solution will be graded on completeness of response (make it convincing!).