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Time Figure 3.5 \begin{tabular}{ccccc} Period & \multicolumn{4}{c}{ Quantity } \\ \hline & 12 & 34 & 56 & 78 \\ \hline & & \multicolumn{4}{c}{ Historical Costs } \\ -4 & 10.00 & 8.00 & 7.00 & 6.50 \\ -3 & 10.70 & 8.60 & 7.50 & 7.00 \\ -2 & 11.10 & 8.95 & 7.80 & 7.20 \\ -1 & 11.25 & 9.00 & 7.90 & 7.30 \\ 0 & 12.00 & 9.65 & 8.40 & 7.85 \end{tabular} 3. The amount of material used by a single job, J, at time t,JJ(t) showing the total material used. The vertical difference between plots TS(t) and TU(t) at a given time period indicates the current amount of inventory on hand. For example, at period t=1,TS(t 1)=10 and TU(t=1)=6, the current inventory =4. Immediately after this point, there is a jump in the total supply by 6 units. The JJ(t) requirement and all other jobs in progress (not shown) total up to the issues for period t on the TU (t) curve. With this as background, recognize the following: TS(t)= total supply of material in inventory at time t, units TU(t)= total usage of material for all jobs at time t, units JJ(t)= total usage for job J at time t, units To the right of period 0 , each of the functions represents inventory projections The step sizes at each of the integer times represent the amount of material going into or out of inventory for that time period. To illustrate, at time 3 the estimated inventory receipts TS(3) will be 2 units while 2 units for TU(3) are expected to be issued, 1 of which goes to job J. A total of 3 units, TS(3)-TU(3), remain in inventory at time 3

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