2. An item is manufactured to meet known demand for four periods according to the following data:

Unit production cost ($) for period Production range (units) 1 2 3 4 1-3 1 2 2 3 4-11 1 4 5 4 12-15 2 4 7 5 16-25 5 6 10 7 Unit holding cost to next period ($) .30 .35 .20 .25 Total demand (units) 11 4 17 29

(a) Find the optimal solution, indicating the number of units to be produced in each period.

(b) Suppose that 10 additional units are needed in period 4. Where should they be produced? .