Alpha manufacturing must decide on a production plan to produce 1650 units of control panels. They have five machines. If machine 1 is used, its production will be between 300 and 1500 units. If machine 2 or machine 3 are used, they can produce up to 1200 and 800 units, respectively. Machine 4 can be used with no restrictions and if we use machine 5, there is a minimum production of 100 units due to its high fixed cost. Machine 1 and 4 cannot be used together due to their high pollution rates. In addition, the total pollution generated by selected machines cannot exceed 20 units. There is a fixed cost associated with setting up each machine and a maximum budget of 1700 on the total fixed cost is set. The fixed cost along with the variable cost per panel are shown in the following table:

Machine	Fixed cost	Variable cost	Minimum Production	Maximum Production	Pollution
1	500	2.00	300	1500	8
2	800	0.50	0	1200	6
3	200	3.00	0	800	3
4	50	5.00	0	any	9
5	700	1.00	100	any	2

Develop an integer program to help Alpha manufacturing decide which machines to use for panel production and how many panels need to be produced under each machine to minimize total cost.

11) define decision variable

12) write down objective function

13) write down constrainst