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stira [4]
3 years ago
12

Which of the following statements are true of a transversal? It is a line. It can be perpendicular to other lines. It intersects

two or more coplanar lines. It bisects line segments. It cannot be parallel to other lines.

Mathematics
2 answers:
aleksandr82 [10.1K]3 years ago
7 0

Answer:

True statements about transversal are as follows:

  1. It is a line
  2. It can be perpendicular to other lines.
  3. It intersects two or more coplanar lines.

Step-by-step explanation:

Transversal :

Transversal is a line which intersects two or more parallel lines which lies in same plane. transversal line crosses the two parallel lines at right angle that time it is called as perpendicular transversal.

As shown in figure AB and CD are two parallel lines which lies in same plane.EF is a line which crosses lines AB and CD at point P and Q respectively. EF is known as transversal line

In figure,

\angle 1= \angle3\\\angle2=\angle4

True statements about transversal are as follows:

  1. It is a line
  2. It can be perpendicular to other lines.
  3. It intersects two or more coplanar lines.

pogonyaev3 years ago
3 0
Its a line, and it intersects two or more coplanar lines
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Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) <u>Optimal solution</u>: 40.000 units of R and 10.000 of PC = $17.000

c) <u>Slack variables</u>: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) <u>Binding Constaints</u>:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

3 0
3 years ago
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