The Northwest Flower Company Owns a Greenhouse, Which Supplies Roses

The Northwest Flower Company owns a greenhouse, which supplies 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 4 square feet and each bunch of carnations about 5 square feet. A special fertilizer is required for the flowers: roses need 5 pounds and carnations 2 pounds. The availability of the fertilizer is limited to 5000 pounds. Sales commitments require the company to grow at least 500 bunches of roses. Profit contributions are $6 per bunch of roses and $8 per bunch of carnations.
a. What is the objective function if the company wants to maximize its profits?
b. What is the constraint for the square footage assuming x₁ corresponds to roses?
c. What is the optimal solution point for this problem?
d. What is the optimal value of the objective function?