The company Connect manufactures various devices that are sold throughout the country. We want to establish a manufacturing program for one of their most famous appliances for the next six months. The sales department has estimated that the demand for the next six months would be as follows:

Months	Demand in units
1	400
2	600
3	750
4	800
5	500
6	625

The production department can manufacture this device on two types of shifts: regular or extra. The maximum production capacity in regular shift is 20 units and 8 additional units in extra shift for one working day. The following table shows the number of working days per month for the next six months:

Months	Number of working days for the month
1	20
2	18
3	19
4	21
5	21
6	20

The manufacturing costs are $20 per unit for regular shifts and $35 per unit for extra shifts. In addition, the company can also store part of its production at a cost of $15 per unit in their in their warehouse which has a capacity of 600 units. At the beginning of this production cycle, the company has 450 units of this device in its warehouse and would like to have a stock of 200 units at the beginning of this production cycle. At the end of the sixth month, the company would like to have a total stock of 200 units.

1. Draw a network that allows Household Appliances to model this multi-period production problem as being production problem as a minimum cost problem. Identify clearly the nodes, the arcs, as well as the capacities and the costs.

2. Since the objective is to minimize the total cost, propose a linear model corresponding to this to this network. Clearly identify the decision variables, the objective function and the constraints of the model.

3. Using the Excel solver, solve this model.