Write the formulations out algebraically for the objective function and constraints. ack Barnet is responsible for purchasing canned goods for the food services at a large university. He knows what the demand will be for cases over the course of the school year and he has estimate purchase prices as well. These data are shown in the table below. He may pre-purchase and carry inventory but there is a cost of $0.20 per case per month for inventory left at the end of each month. Formulate the problem to help Jack solve this. (Hint, for months t=19, let Pt = purchase decision and It = resulting inventory)

Oct 900 Nov 850 Dec 500 Jan 600 Feb 1000 Mar 1000 Apr 1000 May 500 Sept Demand 1000 (in cases) Purchase 20 cost per case that month ($) 20 20 21 21 21 22 22 22