A patient is required to have at least 60 milligrams of nife

A patient is required to have at least 60 milligrams of nifeldipin, at least 1100 micrograms of hydrochloride, at most 1000 micrograms of diezepamum and at least 31 of ibupro-fen both substances are to be consumed by taking a certain amount of Vianol and Gantri of which contain unwanted sodium-sulphate. Each gram of Vianol contains 140 micrograms of diezepamum, 13 milligrams of ibuprofen, micrograms of hydrochlorid, 20 nifeldipin, and 23 milligrams of sodium-sulphate. Each gram of Gantric contains 100 micrograms of diezepamum, 3.5 milligrams of ibuprofen, 310 micrograms of hydrochloride, 15 milligrams of nifeldipin, and 12 milligrams of sodium-sulphate. How many grams of Vianol and Gantric should be taken to the requirements for diezepamum, ibuprofen, and ni and to minimize the intake of sodium-sulphate? l. What is the objective function? 2. Write the constraints. 3. Which optimization method is appropriate for this problem? 4. Solve the problem Note that 1000 microgram F 1 milligram.

Solution

x1 x2 x3 x4 x5 Diezepamum Ibuprofen Hydrochlorid Nifeldipin Sodium sulphate Vianol X 140 13000 705 20000 23000 56845 gantric Y 100 3500 310 15000 12000 30910 min amt 31000 1100 60000 13000x+3500Y >=31000 705X+310Y >=1100 20000x+15000Y >=60000 Minimise z = 23000x+12000Y Thus to get the minimum x should be atleast 3 and y should be atleast 8.857 Sodium sulphate minimum taken = 69000+106284=175284