1. Consider the following linear programming problem: Maximize: P = 12x1 + 10x2 subject to: 5x1 + 3x2 15 x1 + x2 4 x1 0, x2 0 1.1 Using slack variables, convert the system of inequalities (i-system) into a system of equations (e- system). 1.2 Using the table method, fill in the following table. x1 x2 s1 s2 P = 12x1 + 10x2 Feasible? Yes or No 0 0 0 0 0 0 0 0 0 0 0 0 1.3 What is a maximum value of P? What are the values of x1 and x2 that lead to the maximum value of P? 2. Use the simplex method to solve the problem: Maximize: P = 3x1 + 2x2 subject to: 5x1 + 2x2 20 3x1 + 2x2 16 x1 0, x2 0 3. A farmer has 640 acres to plant in corn and soybeans. Each acre of corn requires 45 labor-hours and each acre costs $100 in seed and fertilizer. Each acre of soybeans requires 60 labor hours and each acre costs $80 in seed and fertilizer. The farmer estimates that he has 36,000 hours of labor and $60,000 capital to spend. The farmer estimates that each acre planted in corn will yield a profit of $120 and each acre planted in soybeans will yield a profit of $100. Under these conditions, how many acres of corn and how many acres of soybeans should the farmer plant to maximize his profit? Note: Use the simplex method to solve the problem.