During the busiest season of the year, Green-Gro Fertilizer produces two types of fertilizers. The standard type (X) is just fertilizer, and the other type (Y) is a special fertilizer and weed-killer combination. The following model has been developed to determine how much of each type should be produced to maximize profit subject to a labor constraint:
Maximize profit = 12X – 0.04X2 + 15Y - 0.06Y2
subject to 2X + 4Y ≤ 160 hours
X, Y ≥ 0
Find the optimal solution to this problem.