Use the Simplex method to solve the linear programming probl

Use the Simplex method to solve the linear programming problem. Maximize z = 15x_1 + 4x_2 subject to: 5x^+ 2x2 alt lessthanorequalto 7 X1 + 2x2^5 with x1 alt lessthanorequalto 0, x2 alt lessthanorequalto 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The maximum is when x1 = x2 = s1 = 0. and s2 = 18/5. (Reduce any fractions to lowest terms.) There is no maximum solution to this linear programming problem.

Solution

z = 15x1 + 4x2

5x1 + 2x2 <= 7

x1 + 2x2 <= 5

x1>=0 , x2>=0

corner points of the constraints are

(0,2.5 ) , (.5,2.25) , (1.4,0) and (0,0)

at (0,2.5)

z = 15(0) + 4(2.5) = 10

at (.5,2.25)

z = 15(.5) + 4(2.25) = 16.5

at (1.4,0)

z = 15(1.4) + 4(0) = 21

at (0,0) z = 0

hence, z is maximum when x1 = 1.4 , x2 = 0 , maximum = 21