Show that the decision version of the knapsack problem is np-complete. (hint: in your reduction, make use of the partition problem: given n positive integers, partition them into two disjoint subsets with the same sum of their elements. the partition problem is np-complete.)

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.