I would like to understand how to solve this problem.

Problem 1: 4. The Fit Corporation makes two types of widgets that are sold at a retail store. Demand for the widgets (each week) is as shown below: Demand (units) Widget 1 Widget 2 100 0.2 0.2 200 0.2 0.3 300 0.5 0.3 400 0.1 0.2 Thus Fit faces an average demand of 250 widgets per week for each of the two widgets. The widgets cost $40 per unit to produce. The retail price is $70 per unit. All orders are placed by the retail store at the start of the week and are delivered immediately to the store. If the retail store runs out of stock, Fit purchases a widget from a competitor at a cost of $100 per widget and supplies it to the customer. The customer pays (as before) a price of $70 per widget. Weekly holding cost is 10% of the cost of the widget. Yearly demand for widgets is 13,000 widgets. 4a. Assume that Fit's retail store places orders once a week. Provide an inventory for each product and associated average inventory level at the store. 4b. An engineer at Fit has figured out a way to produce a generic widget that can perform the functions of the earlier two widgets. Thus Fit's retail store would have to store only one SKU of this new widget and yet satisfy all of the demand for the two widgets. Assume that the demand distributions remain the same as in 4a and that customers are willing to use the new widget instead of the old widgets. Production cost of this new widget is still $40. The other costs are as before. Assume that Fit's retail store follows a weekly ordering policy, and provide an inventory policy for the new widget and the associated average inventory level at the store. 4c. Does the total average retail inventory level (across all widgets) decrease if Fit adopts the new widget to satisfy demand? Explain