The production-planning data for an aggregate product are given in the Table below.

Month	Demand (units)	Production Cost ($/unit)	Capacity (units)
January	30	2.1	90
February	50	3.2	90
March	150	1.5	120
April	50	2.75	100
May	85	2.7	115

10% of the production in any one month is defective and, therefore, cannot be used to satisfy demand. Units of the product can be stored in inventory. There will be 10 units in stock at the beginning of January and it is required to have a stock of 15 units at the end of May. It costs $0.2 per month to hold one unit in stock.

1. Build and solve an Excel model to find the optimal production plan, with the objective of minimizing total cost. Write down the optimal production plan and the optimal cost. [15 Points]

2. Copy the base model again to a new spreadsheet in your workbook and extend it to handle the following additional features (data are in the table below):
   • There is a fixed charge for setting up production in any one month, as shown below.

Month	Setup Cost ($)
January	50
February	60
March	70
April	80
May	90

• If production is initiated, the number of units produced must be no less than 30.

The objective is again to minimize the total cost. Solve the model and write down the production plan and the optimal cost.