A canned soup manufacturing operation is in need of advice regarding the sizing of production facilities. They have acquired demand data from their retail partner. The retailer has maintained fixed pricing on all canned soup products and its assumed there are no seasonality or cyclical influences on soup demand. However, there is some variation, which needs to be accounted for when making production decisions. At first, you will consider two products, A and B across three stages of production (canning, labelling, and inspection). Demand data for each product over the Time (weeks) (A) 1 85 2 74 3 39 4 88 5 71 6 71 7 94 8 42 9 33 10 52 11 35 12 23 13 36 14 93 15 92 16 80 17 35 18 92 19 56 20 69 last 20 weeks is shown below. Demand Demand (B) 237 179 246 158 107 214 137 178 133 217 133 123 151 268 103 280 168 286 105 190 At this point, the retailer is tasked with which forecast to use, and how much to order for each product. Generate at least three different forecasts for each product (one of these should be based on a single linear regression of demand (as the dependent variable) and time (as the independent variable). Calculate the EOQ for each product and each forecast assuming demand for Time=21 is given by each calculated forecast. Also, the cost of ordering for the retailer is $13 per order, and the inventory holding cost at the retailer is $0.25 per can of soup. The owners of the manufacturing operation have expressed a preference for the forecast with the least variance. Given that the cost of changing production rates is very large. Given this information; Select the most appropriate forecast for the manufacturing operation. Make sure you justify your selection by quantitative and qualitative means (hint: you may want to calculate the variance and standard deviation of each forecast, and dont forget the regression-based forecast!). issuing orders to the manufacturer, but is unsure Given this choice of forecast, what is the most appropriate inventory management policy (i.e., order size and frequency) and what other choices need to be evaluated if this policy where to be taken forward? On the manufacturing side, each can of soup must go through three stages of the manufacturing process: cooking, a canning and labelling (which occurs at the same time), and inspection. Each can of A requires 18 seconds of cooking, 2 seconds of canning/labelling, and 1 second of inspection. Each can of B requires 15 seconds of cooking due to its difference in consistency, 2 seconds of canning/labelling and 1 second of inspection. The selling price per can of A is $1.70 while the selling price per can of B is $1.50. Currently, each week there are 4 hours of processing time available (split across each stage as 60% of the time is available for cooking, 20% for canning/labelling, and 20% for inspection. The minimum batch size for each product is also important as no less than 50 cans of A and 100 cans of B can be produced in any given production periods. Linear programming is to be used to develop a production schedule to determine how many cans of A and B are produced in the time available. Given these production constraints, present a linear programming formulation, present all feasible solutions and compare them to the demand data and EOQ quantities developed in the previous parts of the report. Finally, present the soup operation with a recommendation of how to size the production facilities. Ensure you provide justification for your recommendation.