Annual Demand $=200,000$

The order cost $=$$$100$

Annual holding rate $=25\%$

Price varies depending on the order quantity per the following schedule:

Orders between $1$ to $50,000$ units cost $$11$

Orders of $50,001$ to $150,000$ cost $$10\mathrm{.}75$

Orders greater than $150,000$ cost $$10\mathrm{.}50$

Determine the optimal order quantity using the price discount model discussed in class. Show all your work.