Hint: This problem can be done with less than 150 variables and less than 110 constraints. PROBLEM DESCRIPTION WM Industries operates Mo manufacturing plants that produce three products: Widgets, Gadgets, and Flugels. The nished products are shipped to the Distribution Center for nal distribution to the customers. Five periods of production are to be sdteduled. According to the Sales Department, the production requirements that must be met due to contracts during the planning horizon are as follows: Product Periodl PeriodZ PeriodB Period 4 Period5 Widgets 70 125 185 190 200 Gadgets 200 300 295 245 240 Flugels 140 1:75 205 235 230 Also, the Marketing 8: Forecasting Department anticipates that WM industries can cultivate additional demand within the distribution area through effective advertising. The MBrF Department projects that each $150 invested in advertising Widgets in a particular period creates additional demand for one Widget in the next period. The corresponding values for Gadgets and Flugels are $120 and $130, respectively. However, the total advertising budget is limited to $?0,000 for the entire planning horizon. Throughout the planning horizon, WM Industries will sell 'Widgets for $2490, Gadgets for $1990, and Flugels for $2970. The products can be manufactured at either of WM's Manufacturing Plants. The Engineering Department has provided the following manufacturing and inventory data. Plant A The production requirements at PlantA are summarized below. ' Each Widget requires 194 pounds of Raw Material 1, 8.5 pounds of Raw Material 2, and 9.5 hours of Labor. ' Each Gadget requires 230 pounds of Raw Material 1 and 2.1 hours of Labor. I Each Flugel requires 178 pounds of Raw Material 1, 11.6 pounds of Raw Material 2, and 11.1 hours of Labor. Regular time labor availability is limited to 2500 hours in each period, but overtime can be scheduled in any amount if necessary. Labor costs during periods 1 and 2 are $11i'hour for regular time and $16.50r'hour for overtime. Labor costs are expected to rise by 5% at the end of period 2. The product inventory area can store a combined maximum of 70 units, and inventory costs are as follows. It costs $7.50 to store one Widget from one period to the next. The corresponding costs for Gadgets and Flugels are $5.50 and $6.50, respectively