Please work out in excel and show steps in excel. Your company manufactures printer cases on two different injection molding machines. The M$-100$ has a capacity of $25$ cases per hour, and the M$-200$ has a capacity of $40$ cases per hour.

Both machines use the same chemicals in the manufacturing process; the M$-100$ uses $40$ pounds of material per hour, and the M$-200$ uses $50$ pounds per hour.

Your client has asked you to produce as many cases as possible next week, and they will pay $$18$ for every case you can deliver.

Unfortunately, you had scheduled maintenance down$-$time for both of your machines next week, so the M$-100$ will only be available for $15$ hours maximum, and the M$-200$ will only be available for $10$ hours maximum. However, due to the high setup costs, if you run either machine during the week, they must run for a minimum of $5$ hours.

That last sentence has the potential to make this an interesting problem.

The operating costs of the machines are $$50/$hour for the M$-100$ and $$75/$hour for the M$-200.$

Your chemical supplier has $1000$ pounds of chemicals available next week at a cost of $$6$ per pound.

What is your business decision for next week, and how much profit will it generate?