AP is a shipping service that guarantees overnight delivery of packages in the continental US$.$ The company has various hubs at major cities and airports across the country. Packages are received at hubs, and then shipped to intermediate hubs or to their destination. The manager of the AP hub in Cleveland is concerned about labor costs and is interested in determining the most effective way to schedule workers. The hub operates seven days a week, and the number of packages it handles varies from one day to another. The table below provides an estimate of the number of workers needed each day of the week.

Questions

The manager wants to keep the total wage expenses as low as possible while ensuring that there are sufficient number of workers available each day.

$1.$Formulate the problem.

$2.$Solve the problem in R markdown.

$3.$Find the total cost and the number of workers available each day.

Hint: The number of available workers each day can exceed, but cannot be below the required amount