(Wagner–Whitin for Aircraft Engines) The Pratt & Whitin Company, which
manufactures aircraft engines, needs to decide how many units of a particular bolt to order
in order to build engines over the next 4 months. Orders for engines are placed over a year
in advance, so the company knows its near-term demand exactly; in particular, the number
of engines to produce in the next 4 months will be 150, 100, 80, and 200 in months 1
through 4, respectively. Each engine requires a single bolt. Orders for bolts incur a fixed
cost of $120, and bolts held in inventory incur a holding cost of $0.80 per bolt per month.
Find the optimal order quantities in each period and the optimal total cost.