Can generate for me some questions concerning about linear programming in maths ?

Here are some questions concerning linear programming:

1. A company produces two products, A and B. Product A requires 2 hours of machine time and 1 hour of labor. Product B requires 1 hour of machine time and 3 hours of labor. The company has 100 machine hours and 150 labor hours available per week. The profit for product A is $5 per unit, and the profit for product B is $7 per unit. Formulate this as a linear programming problem to maximize profit.

2. Maximize the objective function P = 3x + 5y subject to the constraints: x + 2y ≤ 20 3x + y ≤ 30 x ≥ 0 y ≥ 0

3. A farmer has 200 acres of land to plant corn and wheat. The cost to plant corn is $30 per acre, and the cost to plant wheat is $20 per acre. The farmer has a budget of $5000. The expected profit from corn is $100 per acre, and from wheat is $80 per acre. How many acres of each crop should the farmer plant to maximize profit?

4. Minimize the objective function C = 4x + 2y subject to the constraints: x + y ≥ 10 2x + y ≥ 12 x ≥ 0 y ≥ 0