this is for IE, operations research: linear M

Kleanex Inc. is a water treatment station where wastewater is received and treated before being discharged in a river. The mass of bio-solids obtained from the process is sold as fertilizer to farmers. The cost to produce 1 ton of fertilizer varies from month to month. The production costs and demand for the next four months are shown in Table 2. Kleanex can produce up to 100 tons of fertilizer per month. It also has the option of holding inventory from one month to the next for a holding cost of $20 per ton per month. Furthermore, unsatisfied demand in a month can be filled in later periods at the cost of $30 per ton per month-delay. To prevent the stench of the fertilizer from reaching unbearable levels, Kleanex Inc. has decided not to hold a batch of fertilizer for more than two months (including the month of production). Kleanex Inc. would like to know how much to produce each month and how much to carry in order to satisfy demand at minimum cost. 1. Formulate this problem as a transportation model. ( 5 pts) 2. Solve the model. ( 2 pts) Same as above, but unsatisfied demand in a month can be filled by a subcontractor who charges $30 per ton above the in-house production costs. Also, it is assumed that no amount of fertilizer will be stored beyond two months (first produced first shipped to customer). Initial and final inventories are zero. 3. Formulate the new problem as a multiperiod model. ( 5pts) 4. Solve this multiperiod model (3 pts)