PROBLEM$-2.(25$ Pts$)$

An industrial engineer in the production planning department of an automotive industry company is in charge of determining the lot sizes of the semi product $K$ in the A single inventory item is ordered from an outside supplier.

The industrial engineer is using Winters's method to forecast the quarterly product sales. He$/$she has been using smoothing constants of $=0\mathrm{.}2,=0\mathrm{.}2$ and $=0\mathrm{.}1.$ He$/$she has currently obtained the following values of the various slope, intercept, and seasonal factors: $S_{10}=240,G_{10}=28,c_{10}=1\mathrm{.}3,c_9=1\mathrm{.}2,c_8=0\mathrm{.}7,$ and $c_7=0\mathrm{.}8.$

a$.$ Determine the forecast for the product sales in quarter $11,12,13$and $14(6$ Pts$)$

b$.$ Current inventory of this item is $15,$ and ending inventory should be $20.$ Assume a holding cost of TL $2$ per period and a setup cost of TL $40.$ Determine the order policy for this item based on the forecasted demand over the next $4$ quarters and ${14}^{th}$ quarters