During nesting season, two different bird species inhabit a region with area 180,000 m2. Dr. Chan estimates that this ecological region can provide 72,000 kg of food during the season. Each nesting pair of species X needs 39.6 kg of food during a specified time period and 120 m2 of land. Each nesting pair of species Y needs 69.6 kg of food and 90 m2 of land. Let x represent the number of pairs of species X, and let y represent the number of pairs of species Y.
a. Describe the meaning of the constraints x 0 and y 0.
b. Describe the meaning of the constraint 120x + 90y 180000.
c. Describe the meaning of the constraint 39.6x + 69.6y 72000.
d. Graph the system of inequalities, and identify each vertex of the feasible region.
e. Maximize the total number of nesting pairs, N, by considering the function N = x + y.