Problem 2 Consider the inspection scheduling problem 'oni the lecture. Consider the case where there are ve stages of production and the parameters of the problem are as follows. (1] The production line involves B = l units, none of which start out being defective. {2] The perunit processing cost p,- at stage t is $113, i = 1, 2,. . . ,5. [3] The probability.r of a unit becoming defective org: in stage t is .1, i. = 1,2, . . . ,5. (4) The xed cost jig,- associated with inspecting in stage 3' given that the last inspection was in stage i is [j t]f2, for j = 1, 2, . . . , 5 and i = CI, 1, .. . , j. (a) The per-unit inspection cost gt, associated with inspecting in stage j given that the last inspection was in stage: is [j -a.'], forj = 1,2,...,5 and i=,1,...,j. 1. Following the discussion in class, lets assume that the hatch will be inspected after the last stage of production. Draw the directed network for the shortest path problem whose solution identies an optimal tradeoff between inspection costs and the costs associated with processing defective units