SUBJECT: MATH - OTHER

Solve the following problems completely. 1. A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a large bookcase and 2 hours to make a small one. The profit on a large bookecase is P350 and on a small bookcase is P200. The carpenter can spend only 32 hours per week making bookcases and must make at least 2 of the large and at least 4 of the small each week. How many small and large bookcases should the carpenter make to maximize his profit? What is his profit? 2. In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4g of protein. But the rabbits should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs P200 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of P300 per ounce. What is the optimal blend of Food X and Food Y? 3. Last year, a city had three school districts: North with a population of 5200 children, South with a population of 10600 children, West, with a population of 15100 children. Use Hamilton, Adams, Jefferson, Webster, and Hill-Huntington methods to apportion 50 speech therapists among the districts