Here is a process I encourage you all to use. Start withexcel spreadsheet and work through total costcalculations. I am showing cost calculation for one combination. You can do the rest combinations and determine the least cost option.

This use case needs that you consider total cost of operations (variable + fixed) for all 3 plants, and various combinations of two operational plants. That will allow to judge which has the lowest cost.

Step 1: Forecast demand

Forecast Demand
W1	9000
W2	13000
W3	11000
W4	15000
W5	8000
	Total: 56000

Here is an example of Plants 1 and 2 operational and closing 3

	Variable Costs and Fixed Costs	capacity	production	allocation
Plant 1 Regular	2.8	14000	6000		<=	27000		27000
Plant 1 overtime	3.52				<=	7000	34000	4000
Plant 2 Regular	2.78	12000	5000		<=	20000		20000
Plant 2 Overtime	3.48				<=	5000	25000	5000
Plant 3 Regular	2.72	15000	7500		<=	25000
Plant 3 Overtime	3.42				<=	6000
							59000	56000

We allocate based on costs/unit - 20000 to plant 2 (regular time, $2.78/unit), 27000 to plant 1 (regular time, $2.8/unit), 5000 to plant 2 (overtime, $3.48/unit), and 4000 to plant 1 overtime ($3.52/unit) to make 56000 units.

Step 2: Variable and Fixed cost computation (without distribution costs)

plants 1 and 2	fixed costs	33500
	Variable costs	89680
		73000
	Total variable costs	162680
	Total Costs	196180

Step 3: Distribution costs data

plants	w1	w2	w3	w4	w5
1	0.5	0.44	0.49	0.46	0.56
2	0.4	0.52	0.5	0.56	0.57
3	0.56	0.53	0.51	0.54	0.35
P1
P3
	9000	13000	11000	15000	8000

Step 4: Distribution allocation, row by row, based on minimum cost in each row

plants	w1	w2	w3	w4	w5
1	0.5	0.44	0.49	0.46	0.56
2	0.4	0.52	0.5	0.56	0.57
3	0.56	0.53	0.51	0.54	0.35
P1	0	13000	3000	15000	0
P2	9000	0	8000	0	8000
	9000	13000	11000	15000	8000

Step 5: Compute distribution costs (multiply unit cost * number of units between warehouse/plant combination)

Transportation Cost	26250

Step 6: Total costs

Fixed costs + variable production costs + variable distribution costs

$222430

Now repeat these steps for all combinations plants 1&2, 2&3, 1&3, all plants (1,2,3); and determine minimum cost solution