A plant peat seller produces peat mix with fertilizer, lava stone, sand, compost and perlite. These raw materials have different rates of permeability. The prices of the raw materials used vary considerably during the period. The cost of these raw materials (kg) for 4 periods and permeability rates are given in table 1(.img)

3 different peat mix will be produced during the 4-period production process. Since the prepared mix will be added to already existing soil, every raw material can be used in any amount. Mix-1 should have minimum 4.5% and maximum 6.5% permeability rate. Mix-2 should have at least 4% and at most 6% permeability rate, while the 3rd mix have at least 3.5% and maximum 8% permeability rate.

There is an initial stock of 50kg of each raw material and total stock capacity for raw material is 250kg. Raw material stock cost is $5 for 1kg. Manufacturer has an agreement with a 3rd party warehouse so that the prepared mixes can be stored in this warehouse. The produced mixtures can be produced and stocked before use. The stock cost of the mixture at the 3pl warehouse produced is $20 per kg.

Demand amount for mixes of the retailer to be sold is shown in the table. 

P        1         2        3         4

1      300   260    290    200 

2     350    250    450    300 

3     200    200    190     250

Producer must meet the demand every period. They don’t want to keep the product in stock after the last period sale. Selling price of the product is $ 200. Formulate the mathematical model that maximizes the profit/minimizes the cost.

Transcribed Image Text:

T Fertilizer 1 210 Lava Stone Sand Compost Perlite 220 210 210 190 245 260 220 140 210 3 210 200 140 210 220 210 240 210 150 220 Phs. 9. 6. 4 T Fertilizer 1 210 Lava Stone Sand Compost Perlite 220 210 210 190 245 260 220 140 210 3 210 200 140 210 220 210 240 210 150 220 Phs. 9. 6. 4