Company ZWZ manufactures three products in a serial system; Product XA is manufactured in Stage 1, Product XB in Stage 2, and XC in Stage 3. Product XB has a sales potential in the market; hence, some of it can be sold at the end of Stage 2, and the remaining can be moved to Stage 3. The third stage produces Product XC, and then delivers it to customers. Two units of Product XA produced in Stage 1 are required for each unit of Product XB in Stage 2. In addition, four units of Product XB produced in Stage 2 are required for each unit of Product XC in Stage 3. Stage 1 can only use regular time; however, Stage 2 has the options of using regular time and overtime in manufacturing. On the other hand, Stage 3 has only one alternative, which is subcontracting. The pertinent data are provided below: Stage 3 Stage 1 11 Stage 2 12 No regular time No overtime Unit regular time cost (TL) Unit overtime cost (TL) Unit subcontracting cost (TL) Unit selling price (TL) Unit processing time (hrs) Regular time capacity (hrs) Overtime capacity (hrs) Minimum subcontracting volume (units) Maximum sales volume (units) No overtime No subcontracting No sales 0.07 320 No overtime No subcontracting No sales Formulate the production planning problem of the company as a three-stage model (Define the decision variables explicitly!). Hint: Drawing the system first will help you in modelling. 18 No subcontracting 25 0.09 160 80 No subcontracting 3300 22 30 No regular time No overtime 100 4500