Base Problem Consider the production planning problem where $4500$ units of a certain product are manufactured on eight 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.

The following conditions also apply.

$1.$ For an employee to operate machine $6$ or $8,$ the employee needs special training. There is only one employee who has received that training.

$2.$ Machines $2,3$ and $4$ are physically close together. Therefore, we can only use one at a time. $$

Create an Integer Programming model and solve it using Excel to answer the following questions: $(30$ points$)$

$1.$ How many units should be made on each machine?

$2.$ Which machines need to be setup?

$3.$ What is the cost $($Production and setup$)$ of your solution?