4. A patient is required to have at least 60 milligrams of nifeldipin, at least

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4. 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 milligram of ibupro- fen daily. These substances are to be consumed by taking a certain amount of Vianol and Gantric, both of which contain unwanted sodium-sulphate. Each gram of Vianol contains 140 micrograms of diezepamum, 13 milligrams of ibuprofen, 705 micrograms of hydrochlorid, 20 milligrams of nifeldipin, and 23 milligrams of sodium-sulphate. Each gram of Gantric contains 100 micrograms of diezepamum, 3.5 milligrams of ibuprofen, 310 micrograms of hydrochlorid, 15 milligrams of nifeldipin, and 12 milligrams of sodium-sulphate. How many grams of Vianol and Gantric should be taken to fulfill the requirements for diezepamum, ibuprofen, hydrochloride and nifeldipin and to minimize the intake of sodium-sulphate?
1. What is the objective function? 2. Write the contraints 3. Which optimization method is appropriate for this problem? 4. Solve the problem show all work. 4. 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 milligram of ibupro- fen daily. These substances are to be consumed by taking a certain amount of Vianol and Gantric, both of which contain unwanted sodium-sulphate. Each gram of Vianol contains 140 micrograms of diezepamum, 13 milligrams of ibuprofen, 705 micrograms of hydrochlorid, 20 milligrams of nifeldipin, and 23 milligrams of sodium-sulphate. Each gram of Gantric contains 100 micrograms of diezepamum, 3.5 milligrams of ibuprofen, 310 micrograms of hydrochlorid, 15 milligrams of nifeldipin, and 12 milligrams of sodium-sulphate. How many grams of Vianol and Gantric should be taken to fulfill the requirements for diezepamum, ibuprofen, hydrochloride and nifeldipin and to minimize the intake of sodium-sulphate?
1. What is the objective function? 2. Write the contraints 3. Which optimization method is appropriate for this problem? 4. Solve the problem show all work.
1. What is the objective function? 2. Write the contraints 3. Which optimization method is appropriate for this problem? 4. Solve the problem show all work.

Explanation / Answer

Solutions.

1. Using the Dichotomous Search Method: x = .363 y = 3.6345 increasing the tolerance, you can get closer to the exact answer x = 0.4. Using the Golden Section Search Method:

         x = .403 y = 3.64.

2. Use either Dichotomous or Golden Section search method. You can use a simple if.. else branch to compute the value of f(x) for a given value of x. With the tolerance of 0.02, the golden section method gives you x = 1.01 and y = 2.9999. The exact value of maximum is (1, 3).

3. x = number of cups of X-tar, y = number of cups of N-er-G. Objective: to minimize C = 18x + 20y. Constraints: 58x + 80y 69, 10.5x + 15y 105, 23x + 10y 150, x 0 and y 0. The feasible region has 4 corner points and (5, 3.5) minimizes the cost.

4. X = number of grams of Vignola, y = number of grams of Gastric. Objective f = 23x + 12y. Constraints: 20x + 15y 60, .705x + .310y 1.1, .14x + .1y 1, 13x + 3.5y 31, x 0 and y 0. Get x = 2.04 and y = 1.28. At that point f = 62.28.

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