Ahmed owns camels and sells camel milk in cans. A can will hold 3 liters of milk. To market his products, he brands his products as High-Vitamin and Low-Fat. Camel milk is processed with liquid-based vitamins, and fats and are packed in his farm. From his experience, he decided to blend the High-Vitamin milk with at least 80% milk, 10% vitamin, and 5% fats; and blend the Low-Fat milk with at least 85% milk, 5% vitamin, and at most 5% fats. He earns a profit of AED15 from a can of High-Vitamin milk and AED10 from a can of Low-Fat milk. He has 1,000 liters of milk, 200 liters of vitamin solution, and 100 liters of fat solution. The ratio between the demand for Low-Fat milk to High-Vitamin milk is at least 0.40. He expects he can sell up to 500 cans of milk products. Ahmed wants to know how many cans of milk to produce to maximize profit.
a. Formulate a linear programming model to this problem.
b. Solve this model using computer.