Question 1: Economic Order Quantity, varying t
(a) In class we showed that the average inventory level under the EOQ model was Q/2 when we look over a time period that is a multiple of T. What is this average inventory level over the period of time from 0 to t for general t? Provide an exact expression for this.

(b) Using your expression above, plot the average inventory (calculated exactly using your expression from part a) and the approximation Q/2 versus Q over the range of 1 to 30. Use t=100 and λ=2.

Note that lambda is a keyword in python and using it as a variable name will cause problems. Pick a different variable name, like demand_rate.

You should see that the approximation is quite accurate for large t, like 100, and is less accurate for small t.