Nitrified a hog feedlot operation near Houston Texas blends

Nitrified, a hog feedlot operation near Houston, Texas blends ingredients to make low cost feed for its hogs. Oats and com are the principal ingredients of the hog feed. The current costs for oats and com are 12 cents and 7 cents respectively. Nitrified requires a minimum of 2.000 mineral units. 3.000 caloric, and 4.000 units of vitamins per day for each hog. Each pound of oats supplies 200 mineral units. 100 caloric, and 200 units of vitamins. Each pound of com supplies 100 mineral units. 200 caloric, and 200 units of vitamins. Formulate this problem as a linear programming problem. 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 S8 per bunch of roses and S6 per bunch of carnations. Formulate this problem as a linear programming problem.

Solution

Q1.

x = quantity of oats

y = quantity of corn

200x + 100y >= 2000

100x + 200y >= 3000

200x + 200y >= 4000

maximise z = 12x + 7y

Q.2

x = bunch of rose

y = bunch of carnations

2x + 3y <= 10000

5x + 2y <= 15000

600 <= x + y <= 750

maximise z = 8x + 6y