9 During the next five periods, the demands in Table 58 must be met on time. At the beginning of period 1, the

inventory level is 0. Each period that production occurs a setup cost of $250 and a per-unit production cost of $2 are incurred. At the end of each period a per-unit holding cost of $1 is incurred.
a Solve for the cost-minimizing production schedule using the following decision variables: xt units produced during month t and yt 1 if any units are produced during period t, yt 0 otherwise.
b Solve for the cost-minimizing production schedule using the following variables: yt’s defined in part

(a) and xit number of units produced during period i to satisfy period t demand.
c Which formulation took LINDO or LINGO less time to solve?
d Give an intuitive explanation of why the part

(b) formulation is solved faster than the part

(a) formulation.

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TABLE 58 Period 1 2 3 4 5 Demand 220 280 360 140 270