Question

olve the following Math model graphically:

X: # of tables to produce

Y: # of chairs to produce

                    Max Z =  OMR 300 X  +  OMR 500 Y 

Subject to:
                          X <= 4
                          Y <=  6
                      3x + 2Y <= 18

Answer 1

Steps to follow for plotting Graph:

Step 1

Plot graphs X= 4; Y= 6 and 3X +2Y=18 on graph

To plot third graph simplify it as in X/6 + Y/9 =1 (by deviding both side by 18)

which means this graph will touch X axis at X = 6 (Point 6,0) and Y axis at Y=9 (Point 0,9).

Step 2

Find out point of intersection between two graphs at a time

a) X=4 & Y = 6 intersect at point (4,6)

b) X=4 & 3X+2Y =18 will intersect at (4,3)

3*4 +2*Y =18

2Y = 18-12

Y=6/2 = 3

c) Y=6 and 3X+2Y = 18 will intersect at (2,6)

3X + 2*6 =18

3X = 18-12

X = 2

Step 3

Critical Points of Graph

All the points of intersection of graph is critical points and could be solution points for us.

There are total five critical points as given below

(0,0) ; (0;6) ; (2,6) ; (4,0) ; (4,3)

Step 4

Find Value of objective function at each of the critical points

Objective Function : Max Z = 300X + 500Y

at (0,0)

Z = 0

at (0,6)

Z= 300*0 + 500*6 = 3000

at (2,6)

Z= 300*2 + 500*6 = 3600

at (4,0)

Z = 300*4 + 500*0 = 1200

at (4,3)

Z = 300*4 + 500*3 = 1200 +1500 = 2700

Step 5

Solution Point : (2,6) as it gives maxm value

Z = 3600

Hence 2 tables and 6 chairs should be produced to maximise profit.