Observe the numbers in the equation and formulate the following problems:
1. Nutrifeed, a hog feedlot operation near Houston, Texas blends ingredients to make low-cost feed for its hogs. Oats and corn are the principal ingredients of the hog feed. The current costs for oats and corn are 12 cents and 7 cents respectively. Nutrifeed requires a minimum of 2,000 mineral units, 3,000 calories, and 4,000 units of vitamins per day for each hog. Each pound of oats supplies 200 mineral units, 100 calories, and 200 units of vitamins. Each pound of corn supplies 100 mineral units, 200 calories, and 200 units of vitamins. Simply Formulate this problem as a linear programming problem.
2. The Northwest Flower Company owns a greenhouse, which furnishes roses and carnations to florists in Oregon, Washington, and Idaho. The greenhouse can grow any combination of the two flowers. They sell the flowers in "bunches" with 25 blooms to a bunch. They have 10,000 square feet available for planting this year. Each bunch of roses takes about 2 square feet and each bunch of carnations about 3 square feet. Special fertilizer is required for flowers: roses need 5 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 15,000 pounds. Management believes that it can sell at least 600 bunches of roses but not more than 750 bunches. Profit contributions are $8 per bunch of roses and $6 per bunch of carnations. Simply Formulate this problem as a linear programming problem.