Hint to draw constraints 1. To draw constraint 44 x 1+33 x 23636(1) Treat it as

Question

Hint to draw constraints

1. To draw constraint 44x1+33x23636(1)

Treat it as 44x1+33x2=3636

When x1=0 then x2=?

44(0)+33x2=3636

33x2=3636

x2=363633=110.18

When x2=0 then x1=?

44x1+33(0)=3636

44x1=3636

x1=363644=82.64

2. To draw constraint 22x1+44x24040(2)

Treat it as 22x1+44x2=4040

When x1=0 then x2=?

22(0)+44x2=4040

44x2=4040

x2=404044=91.82

When x2=0 then x1=?

22x1+44(0)=4040

22x1=4040

x1=404022=183.64

3. To draw constraint 11x288(3)

Treat it as 11x2=88

x2=8811=8

Here line is parallel to X-axis

The value of the objective function at each of these extreme points is as follows:

The maximum value of the objective function z=6920 occurs at the extreme point (84311,8).

Hence, the optimal solution to the given LP problem is : x1=84311,x2=8 and max z=6920.

Explanation / Answer

L.P. Model:

Maximize
Zequals=
88Xplus+22Y
Subject to:
44Xplus+33Yless than or equals3636
(Upper C 1C1)
22Xplus+44Yless than or equals4040
(Upper C 2C2)
11Ygreater than or equals88
(Upper C 3C3)
X,Ygreater than or equals0

1.) Plot and label the constraints
Upper C 1C1,
Upper C 2C2
and
Upper C 3C3
(using the line drawing tool) on the provided graph.
2.) Using the point drawing
tool,
plot the point that maximizes the objective function.
For C1, area
the plotted line is the feasible area
For C2, area to the ___of the plotted line is the feasible area
For C3, area
the
plotted line is the feasible area
012345678910012345678910XYC1C2C
x y graph
For the given constraints, out of the four corner points, three are(0,1), (0,4) and (3.5,1). The fourth corner point is
(3,2)
The objective value
                                               at (0,1) = 3
                                               at (0,4) = 12
                                               at (3.5,1) = 20.5
                                               at (3,2) = 21.00
The optimum solution is:
                                               X =
3.00
                                   (round to 2nd decimal place)
                                               Y = 2.00 (round to 2nd decimal place)
objective value = 21.00( round to 2nd decimal place)
Enter your answer in the answer box and then click Check Answer.

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