PRODUCTION PLANNING ASSIGNMENT Formulate a linear programming model for the Spring Valley Bottling Company problem. Models solution would tell Spring Valley how to schedule production during November and December (objective is to minimize both the inventory holding and production costs). Define clearly all decision variables used. When calculating unit holding costs account for 4 decimal positions. Bottled water is sold by the Spring Valley Bottling Company in three sizes of bottles; Six packs of 12 oz. bottles and single gallon bottles are sent to grocery store distributors, while five gallon bottles are filled for customers who have delivery service for their water coolers. Planning is now under way to schedule the summer production. It is November 1st and schedules must be developed for production during November and December. Bottles are shipped at the end of each month, and demand and inventory information is shown in the table below

type	current inventory	nov demand	dec demand	dec 31 minimum
six packs	600	2000	25000	400
1 gallon	500	3000	3200	300
5 gallon	100	1600	1600	300

In addition, Spring Valley would like to balance production so that for each size, the difference between November and December production is no more than 200 units (the difference could be either an increase in production between November and December of 200 units, or decrease of 200 units). Production costs, which are shown below, vary due to vacation scheduling and overtime. Inventory carrying cost is 28% of the production cost.

Show solution using solver PRODUCTION COST November December Six packs .50 .55 1 Gallon .20 .28 5 Gallon .37 .42