Problem 2 (10 points): When deriving the optimal solution of the Wagner- Whitin Model, we assume that demand in any given period is served entirely by the production in one period, not by productions in two or more periods in fractions (e.g., demand in period 2 can be served 100% by units produced in periods 1 or 2, but not 50% in each period). Question: Explain why the production plan can remain optimal even if we exclude fractional allocation of demand to productions in multiple periods. hint: You may make the argument by contradiction, i.e., consider any solu- tion that involves serving demand in a given period by units produced in two different periods, and show that the total cost can be reduced or at least stays the same by moving the production of all these units into one period.

Problem 2 (10 points): When deriving the optimal solution of the WagnerWhitin Model, we assume that demand in any given period is served entirely by the production in one period, not by productions in two or more periods in fractions (e.g., demand in period 2 can be served 100% by units produced in periods 1 or 2 , but not 50% in each period). Question: Explain why the production plan can remain optimal even if we exclude fractional allocation of demand to productions in multiple periods. hint: You may make the argument by contradiction, i.e., consider any solution that involves serving demand in a given period by units produced in two different periods, and show that the total cost can be reduced or at least stays the same by moving the production of all these units into one period