1. Consider the production planning problem where 4500 units of a certain product are manufactured on five machines. The setup costs, the production costs per unit and the maximum production capacity for each machine are shown in the table to the right. For an employee to operate machine 6 or 8, the employee needs special training. There is only one employee who has received that training. Formulate the problem as an Integer programming model to determine how much to produce on each machine with the objective of minimizing total cost. Solve using Excel

Machine	Setup Cost	Production Cost per unit	Capacity
1	$1000	10	800
2	5000	2	800
3	2000	5	900
4	4000	5	1200
5	4000	6	1000
6	3000	4	1300
7	6000	1	1000
8	5000	3	1500

Answer the following questions:

How many units should be made on each machine?

What is the cost of your solution?

2. The production manager has received authorization to spend $1500 to improve the performance of the production system. She has identified two ways to spend the money

a. Train another worker to operate machines 6 and 8.

b. Update machine 1 to reduce its production cost. She estimates that the production cost per unit will reduce to $4 per unit, but the setup cost will increase to $2000.

c. Leave things the way they are and dont spend the $5000.

Which option should she choose and why?

Please also provide a copy of the sensitivity and analysis reports. *