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I have submitted this question earlier and was told that additional information is needed. I believe I have put all information from the problem statement into the question so I am not sure what the previous experts are referring to by saying more information is needed. If there is specific information that I need to provide, please let me know if the prompt needs to be updated what information is needed and I will try to figure out what I missed and update the question as soon as possible

Question:

A company has purchased a 35,000sq-ft warehouse and wants to design a three shift, continuous job shop to produce two products, Product A and Product B. The shop is comprised of five groups of machines, each with an identical number of machines: Machine 1 (costs 1.5 million per machine, 60 minute operation time), Machine 2 (costs 5.5 million per machine 20 minute operation time), Machine 3 (costs 2.5 million per machine, 125 minute operation time), Machine 4 (costs 3.5 million per machine, 50 minute operation time), and Machine 5 (costs 2 million per machine, 35 minute operation time).

A new job enters the shop every ten minutes and we know that 46% of jobs entering the shop are for Product A with the remaining 54% being for Product B. Product A must follow the sequence of Machine 1 to Machine 5 to Machine 4. Product B must follow the sequence of Machine 1 to Machine 3 to Machine 5 to Machine 2.

Machines 3 and 5 share a space and, due to a spatial limitation, there can only be a maximum of fourteen machines within that space. Since both Machine 3 and Machine 5 are both needed and since the problem states that there must be an identical number of machines, there can, at most, only be seven of each machine type.

Transporting products from one machine to the next takes five minutes with an average variation of 10%. It also takes five minutes to deliver materials to Machine 1 and to remove the finished product from Machine 4 for Product A or Machine 2 for Product B. The only exception is that the time required to move from Machine 1 to Machine 5 (for product A) is ten minutes instead of five.

If given a budget of 67 million dollars, and knowing that the primary performance measure of interest is the average cycle time of jobs, what are the minimum and maximum number of machines that would be required to optimize the cycle time of the system?