Minimize C = 3x_1 + x_2 Subject to 2x_1 + 3x_2 greaterthanorequalto 60 x_1 + 4x_

Question

Minimize C = 3x_1 + x_2 Subject to 2x_1 + 3x_2 greaterthanorequalto 60 x_1 + 4x_2 greaterthanorequalto 40 x_1 greaterthanorequalto 0, x_2 greaterthanorequalto 0 A) Maximize P = 3y_1 + y_2 Subject to 2y_1 + y_2 lessthanorequalto 3 3y_1 + 4y_2 lessthanorequalto 1 y_1 greaterthanorequalto 0, y_2 greaterthanorequalto 0 B) Maximize P = 60y_1 + 40y_2 Subject to 2y_1 + y_2 lessthanorequalto 3 3y_1 + 4y_2 lessthanorequalto 1 y_1 greaterthanorequalto 0, y_2 greaterthanorequalto 0 C) Maximize P = 3y_1 + y_2 Subject to 2y_1 + y_2 lessthanorequalto 3 3y_1 + 4y_2 greaterthanorequalto 1 y_1 greaterthanorequalto 0, y_2 greaterthanorequalto 0 D) Maximize P = 60y_1 + 40y_2 Subject to 2y_1 + y_2 greaterthanorequalto 3 3y_1 + 4y_2 greaterthanorequalto 1 y_1 greaterthanorequalto 0, y_2 greaterthanorequalto 0

Explanation / Answer

7. Min Z = 3x1 + x2

2x1 + 3x2 >= 60

x1+ 4x2 >= 40

when

2x1 + 3x2 = 60

x1=0

x2 = 20

x2 =0

x1 =30

points are (0,20),(30,0)

A.) Max P= 3y1 + y2

2y1 + y2 <=3

3y1 + 4y2 <=1

when

2y1 + y2 = 3

y1 =0

y2 =3

y2=0

y1 = 3/2

now 3y1 + 4y2 =1

y1 = 0

y2 = 1/4

y2 = 0

y1 = 1/3

so the points are (0,3) ,(3/2,0),(0,1/4),(1/3,0)

D.) Max Q =60y1 + 40y2

2y1 + y2 >=3

3y1 + 4y2 >= 1

when 2y1 + y2 =3

y1 =0

y2 =3

y2 =0

y1 = 3/2

now

3y1 + 4y2 = 1

now 3y1 + 4y2 =1

y1 = 0

y2 = 1/4

y2 = 0

y1 = 1/3

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