Use the simplex method to solve the linear programming problem.Convert linear equations by using slack variables. 8) Maximize z = 2x1 + 8x2 Subject to: x₁ + 6x2 ≤ 15 7x1 + 5x2 ≤ 25 x1 ≥ 0, x2 ≥ 0 a) Convert the constraints into linear equations by using slack variable b) Write the initial simplex tableau using slack variables. c) Find the pivot in the simplex tableau. d) Perform the pivoting for the pivot found in part (c). e) Repeat parts (c) and (d) if necessary to find another pivot. f) Write the basic solution for the simplex tableau determined by settim variables equal to 0.

Part1)An airplane carries water and medical kits to survivors of a natural disaster. The plane can carry a maximum payload of 80,000 pounds. Each container of water weighs 20 pounds, and each medical kit weighs 10 pounds.The cargo space holds a maximum of 6000 cubic feet of cargo. Graph these constraints on the grid provided, and write some units on the axes. Assume each container has a volume of 1 cubic foot. Part2)If each container of water serves 10 people and each medical kit aids 6 people, find the number of water containers and medical kits that could help the most people

Solve the linear programming problem using the simplex method. Maximize P = -x₁ + 2x₂ subject to x₁ + x₂ ≤2 -X₁ + 3x₂ ≤18 X₁-4x2 ≤8 X₁, X₂ 20 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The maximum value of P is P= (Simplify your answers.) OB. There is no optimal solution. when x₁ = *** and X₂=