Reference no: EM132291768
Assignment Questions -
1. The annual production volume (P) of a factory is directly proportional to the capital X invested in the material, and is proportional to the square of the fund Y invested in wages, and is proportional to the cube of the capital Z invested in the machine, that is P = cXY2Z3. Assuming that the existing capital is 12,000,000 dollars, how it should invest in the funds of the materials, the funds of the wages and the funds of the machines for the maximum production.
2. Please prove S = {(x1, x2)∈R2|x1+x2≥1} is a convex set.
3. Answer questions for the following linear programming models
Max Z = 3x1 - x2 + 2x3 + x4
s.t. 3x1 - x2 + 2x3 + x4 ≤ 2
x1 + x2 + 4x3 + x4 ≤ 7
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0
(1) Please use the Simplex method to solve the optimal solution of this linear programming.
(2) Convert the above linear programming model into a dual problem and solve the problem graphically.
(3) Explain (1) and (2), Tell the S differences between the target solution and the decision variable solution.