Solve the following linear programming problems using the graphical solution. And please identify the feasible regions, feasible corner points and the optimal solutions.

1. Profit Maximization for Corn-Soybean Farm (25 points)

Resources Amount Crop Production Enterprise

Constraints Available Corn Soybean

a) Crop land 400 acres 1 1

b) Family labor 225 hours 0.45 0.60

c) Operating capital P 35,000.00 110 60

Net Income per acre P150.00 P140.00

2. Net Return Maximization for Rice-Corn Farm Enterprise (30 points)

Resources Amount Crop Production Enterprise

Constraints Available Corn Rice

a) Crop land 10 acres 1 1

b) Labor for land preparation 75 hours 10 0

c) Labor for planting 200 hours 8 8

d) Labor for harvesting 160 hours 8 20

Net Return per acre P400.00 P300.00

3. Minimization Problem (15 points)

Minimize z = 4x₁ + 3x₂

Subject to: 2x₁ + x₂ ? 10

-3x₁ + 2x₂ ? 6

x₁ + x₂ ? 6

x₁, x₂ ? 0