RJ-Filter Inc. produces home water filters. The production department would like to develop a production schedule to determine the number of units to produce in October, November and December.

The demand for October, November and December are 13,000 water filters, 15,000 water filters, and 18,000 water filters, respectively. The production capacity in October is 13,500 water filters, in November 13,500 water filters, and in December 16,000 water filters. In addition, RJ-Filter has the storage capacity to store up to 5000 water filters at the end of each month. In September, the company produced 15,000 water filters but only sold 10,000, thus 5000 water filters are currently in inventory.

It is desirable to have a production schedule that maintains the current workforce level and has the same production quantities each month. However, given fluctuations in the demand, production capacities, and storage capabilities this may NOT be possible. The companys cost accounting department estimates that increasing the production by one water filter from one month to the next will increase total costs by $1.20 per water filter and decreasing production by one water filter from one month to the next will increase total costs by $0.90 per water filter.

Ignoring production and inventory holding costs, formulate algebraically the linear programming model that will help RJ-filter Inc. determine the number of units to produce in October, November and December that will minimize the cost of changing the production levels while satisfying the monthly demands. DO NOT SOLVE

Hint: cost of changing production levels = cost of the monthly production increases + cost of the monthly production decreases.

Use the following decision variables to formulate your LP model

Xi = the number of water filters produced in month i

Ii = inventory level at the end of month i

di = decrease in the total production level in month i

ei = increase in the total production level in month i

where i = 1, 2 and 3 (1 refers to October; 2 refers to November, and 3 refers to December).