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)

ResourcesAmountCrop Production Enterprise

Constraints AvailableCornSoybean

a)Crop land400 acres11

b)Family labor 225 hours 0.450.60

c)Operating capitalP 35,000.0011060

Net Income per acreP150.00P140.00

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

ResourcesAmountCrop Production Enterprise

ConstraintsAvailableCornRice

a)Crop land10 acres11

b)Labor for land preparation75 hours 100

c)Labor for planting200 hours8 8

d)Labor for harvesting160 hours8 20

Net Return per acreP400.00P300.00

3.Minimization Problem (15 points)

Minimize z = 4x₁+ 3x₂

Subject to: 2x₁+ x₂ 10

-3x₁+ 2x₂ 6

x₁+ x₂6

x₁, x₂ 0