Happy Milk Distributors (HMD) purchases raw milk from farmers in Mesudiye and Muradiye. Prices, butterfat content and separation properties of the raw milk differ between the two regions. HMD processes the raw milk to produce cream and milk to desired specifications for distribution to the consumers Milk from Mesudiye is 54 kr. per liter up to 500 liters and 58 krs. per liter in excess of 500 liters. There is no upper bound on the amount that can be purchased. Raw milk from Mesudiye has 25% butterfat and when separated (at 5 kr. per liter) it yields two "milks", one with 41% butterfat and an other with 12% butter fat The volume of milk is conserved in all separation proce ss ing. The purchase price for milk from Muradiye is 38 krs. per liter up to 700 liters and 42 krs per liter thereafter. Raw milk from Muradiye has 15% butterfat and when separated (at 7 kr. per liter) yields two "milks", one with 43% butterfat and another with 5 % butterfat. After the milk is purchased and collected at the plant, it is either mixed directly or separated and then mix ed. The mixing is done at no cost, and its purpose is to produce cream and milk to specifications. For example, some of the raw milk from Mesudiye may be separated and then mixed, and some of it may be mixed directly (i.c., without having been separated). The demand and selling price are given in the following table: Fat %40 Volume Price 250 Cream 1,5 TL Milk %20 2000 0,7 TL Fat: minimum required percent of butterfat Volume: Maximum volume demanded in gallons Price: Selling price in cents per gallon For example, all the cream produced must have at least 40 % butterfat, it sells at 150 TL per liter, and as much as 250 liters of the cream produced can be sold Assuming free disposal, formulate a linear program which would enable HMD to maximize its profit. Happy Milk Distributors (HMD) purchases raw milk from farmers in Mesudiye and Muradiye. Prices, butterfat content and separation properties of the raw milk differ between the two regions. HMD processes the raw milk to produce cream and milk to desired specifications for distribution to the consumers Milk from Mesudiye is 54 kr. per liter up to 500 liters and 58 krs. per liter in excess of 500 liters. There is no upper bound on the amount that can be purchased. Raw milk from Mesudiye has 25% butterfat and when separated (at 5 kr. per liter) it yields two "milks", one with 41% butterfat and an other with 12% butter fat The volume of milk is conserved in all separation proce ss ing. The purchase price for milk from Muradiye is 38 krs. per liter up to 700 liters and 42 krs per liter thereafter. Raw milk from Muradiye has 15% butterfat and when separated (at 7 kr. per liter) yields two "milks", one with 43% butterfat and another with 5 % butterfat. After the milk is purchased and collected at the plant, it is either mixed directly or separated and then mix ed. The mixing is done at no cost, and its purpose is to produce cream and milk to specifications. For example, some of the raw milk from Mesudiye may be separated and then mixed, and some of it may be mixed directly (i.c., without having been separated). The demand and selling price are given in the following table: Fat %40 Volume Price 250 Cream 1,5 TL Milk %20 2000 0,7 TL Fat: minimum required percent of butterfat Volume: Maximum volume demanded in gallons Price: Selling price in cents per gallon For example, all the cream produced must have at least 40 % butterfat, it sells at 150 TL per liter, and as much as 250 liters of the cream produced can be sold Assuming free disposal, formulate a linear program which would enable HMD to maximize its profit
