Q6: Each Internet of Tea Maker requires a heating element. We have found a company that will manufacturer the heating elements. We need 30,000 heaters per month. Unsatisfied demand means we miss out on a sale in that month, costing $200 per unit. The cost of initial manufacturing setup for each production run is $1,000. It costs $20 to produce each heater and the holding cost is $2 per heater per month. The manufacturer can produce 40,000 heaters per month. Warehouse space for the heaters in our production facility is limited to 100,000 heaters. i) Find the minimum-cost procurement quantity and the procurement level under this restriction if the lead time is 5 months. ii) What is the cost penalty per period due to the warehouse restriction?

( the question is from chapter 9 of the book named Systems Engineering and Analysis (5th Edition) )