PLEASE ANSWER WITH FULL DETAIL ON HOW TO SOLVE THIS IN EXCEL, PLEASE PROVIDE ALL EQUATIONS AND SCREENSHOTS PLEASE!! THANK YOU!!

Question $1)$ Consider a machine in a manufacturing center that can process multiple types of products.

During a day, the machine is available for $8$ hours. We have a set of potential items that can be

processed on this machine and after the process, each item can be sold to a customer. Assume that we

only can sell one copy of each item. Table below shows the processing times and the potential profit of

each item.

$1-$ Which items the manufacturer should select to process and sell to the customer to maximize his

profit? Write a mathematical optimization model for this problem. Clearly define decision

variables, objective function, and constraints for the optimization model. Use Excel solver to

solve the optimization model.

Answer:

Notation and definition of the decision variables:

Objective function:

Constraints:

$2-$ How long $($in minutes$)$ the machine remains idle during a day?

Answer: Idle time in minutes:

$3-$ What is the solution of the problem if we assume that we can sell multiple copies of each item?

How the objective function value changes if we consider this new assumption? Use Excel to

solve the problem with this new assumption.

Answer: Value of the objective function with the new assumption: