Question

38. Solve the following LPP graphically. Maximize 2 = 50x + 40y Subject to constraints:
1000x + 1200y < 7600, 12x + 8y < 72, x > 0, y>0
Solve the following LPP graphically. Minimize Z = 5x + 7y Subject to constraints:
2x+y < 8, x + 2y > 10 and x,y > 0​

Answer 1

Step-by-step explanation:

Given:

1000x+1200y < 7600

12x+8y < 72

x>0

y>0

To find:Solve the following LPP graphically. Maximize Z = 50x + 40y Subject to constraints written above.

Solution:

Tip: Convert inequations into equations and plot lines then check with inequality sign whether origin will include or not.

Step 1: Convert 1000x+1200y < 7600 into equation

1000x+1200y = 7600

Find x any y intercept by putting x=0 and y=0 and find respective y and x values.

Points are (0,6.33) and (7.6,0).

Plot these points and draw line,it is obvious that inequation contains origin because 0<7600,thus shade the portion below this line. Graph is attatched for reference.

Step 2: Convert 12x+8y < 72 into equation

12x+8y = 72

Find x any y intercept by putting x=0 and y=0 and find respective y and x values.

Points are (0,9) and (6,0).

Plot these points and draw line,it is obvious that inequation contains origin because 0<72,thus shade the portion below this line. Graph is attatched for reference.

x>0 and y> 0 indicates the first quadrant.

Step 3: Take all boundaries as well as origin (0,0)

All the boundary points are

(6,0)

(0,6.33)

(4,3)

(0,0)

Step 4:To maximize Z put these boundaries into Z and take the points of maximum value.

Z maximize at (4,3)

Z = 50x + 40y

Z=50×4+40×3

Z=200+120

Z=320

Final answer:

Graph is attatched.

Maximum value of Z is 320 at x=4 and y=3.

Hope it helps you.

Remark*: Do the second question by the same process.If find problem then ask that question alone.

To learn more:

1) Solve the following Linear Programming Problem graphically: Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4,...

https://brainly.in/question/8208597

2) Solve the following Linear Programming Problem graphically: Minimise Z = - 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12,...

https://brainly.in/question/8208599