1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
leonid [27]
2 years ago
5

A graph represents the feasible region for the system: y is less than or equal to 2x, x + y is greater than or equal to 45, and

x is less than or equal to 30. What is the minimal number for the objective function P = 20x + 16y? What is the value of x then? What is the value at y then?

Mathematics
2 answers:
atroni [7]2 years ago
6 0
Notation. x  y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means x is greater than y. The last two inequalities are called strict inequalities. Our focus will be on the nonstrict inequalities. Algebra of Inequalities Suppose x + 3 < 8. Addition works like for equations: x + 6 < 11 (added 3 to each side). Subtraction works like for equations: x + 2 < 7 (subtracted 4 from each side). Multiplication and division by positive numbers work like for equations: 2x + 12 < 22 =) x + 6 < 11 (each side is divided by 2 or multiplied by 1 2 ). 59 60 4. LINEAR PROGRAMMING Multiplication and division by negative numbers changes the direction of the inequality sign: 2x + 12 < 22 =) x 6 > 11 (each side is divided by -2 or multiplied by 1 2 ). Example. For 3x 4y and 24 there are 3 possibilities: 3x 4y = 24 3x 4y < 24 3x 4y > 24 4y = 3x + 24 4y < 3x + 24 4y > 3x + 24 y = 3 4x 6 y > 3 4x 6 y < 3 4x 6 The three solution sets above are disjoint (do not intersect or overlap), and their graphs fill up the plane. We are familiar with the graph of the linear equation. The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other side of the line. To determine which side for an inequality, choose a test point not on the line (such as (0, 0) if the line does not pass through the origin). Substitute this point into the linear inequality. For a true statement, the solution region is the side of the line that the test point is on; for a false statement, it is the other side.
lawyer [7]2 years ago
6 0
<h2>Answer:</h2>
  • The minimal number for the objective function P =20x+16y is: 780
  • The value of x then is: 15
  • and the value of y then is : 30
<h2>Step-by-step explanation:</h2>

We are given a system of inequalities as:

y is less than or equal to 2x

i.e.          y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e.      x+y ≥ 45  ------------(2)    

and    x is less than or equal to 30.    

i.e.               x ≤ 30 -----------(3)    

On plotting these inequalities we get the boundary points as:

         (15,30) , (30,60) and (30,15)    

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

 Minimize  P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

  P= 1560

at (30,15) we get:

P= 840

This  means that the minimal value of the function is 780

and the value exist at (15,30)

You might be interested in
A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station. Find the ra
Anika [276]

Answer:

The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

Step-by-step explanation:

Given information:

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.

z=1

\frac{dx}{dt}=430

We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

y=2

According to Pythagoras

hypotenuse^2=base^2+perpendicular^2

y^2=x^2+1^2

y^2=x^2+1               .... (1)

Put z=1 and y=2, to find the value of x.

2^2=x^2+1^2

4=x^2+1

4-1=x^2

3=x^2

Taking square root both sides.

\sqrt{3}=x

Differentiate equation (1) with respect to t.

2y\frac{dy}{dt}=2x\frac{dx}{dt}+0

Divide both sides by 2.

y\frac{dy}{dt}=x\frac{dx}{dt}

Put x=\sqrt{3}, y=2, \frac{dx}{dt}=430 in the above equation.

2\frac{dy}{dt}=\sqrt{3}(430)

Divide both sides by 2.

\frac{dy}{dt}=\frac{\sqrt{3}(430)}{2}

\frac{dy}{dt}=372.390923627

\frac{dy}{dt}\approx 372

Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

6 0
3 years ago
First to help gets marked brainliest!!
Lubov Fominskaja [6]

Answer:

x: -8, -4, 0, 4

y:  6,  4,  2,  0

Equation: y = 2 - 0.5x

7 0
2 years ago
((help? just a bit of help!))
Monica [59]
Find the common denominator of 6 and 4.
6: 6, 12...
4: 8, 12...

We can use 12 for this example.

5/6 to ?/12.
12 / 6 = 2, therefore do 5 x 2.
5 x 2 = 10. 10/12.

1/4 to ?/12.
12 / 4 = 3, therefore do 3 x 1.
3 x 1 = 3. 3/12.

13/12. 1 1/12.

I believe you ran out of space or didn't put answer D. I researched this question and concluded that the other choice is 1 and 1/12.

The answer is 1 and 1/12.
5 0
3 years ago
A pizza is to be cut into halves. Each of these halves is to be cut into sevenths. What fraction of the pizza is each of the fin
Hitman42 [59]

Answer: \dfrac{1}{14}

Step-by-step explanation:

Given, A pizza is to be cut into halves.

Since half is represented by \dfrac12 .

So each piece is now \dfrac12 of the original.

if each of these halves is to be cut into sevenths, then the fraction of  final pieces would be: \dfrac{1}{2}\times\dfrac{1}{7}=\dfrac{1}{14} or we can say each half is divides into 7 pieces since there are two halves, so there will be 2 x 7 = 14 peices.

And the fraction of the pizza is each of the final pieces = \dfrac{1}{14} .

7 0
3 years ago
Three times a number increased by 8 is no more than 24
Naily [24]

Answer:

3x + 8 ≤ 24

Step-by-step explanation:

Three times a number

3x

increased by 8

+ 8

no more than 24

≤ 24

---------------------

Altogether

3x + 8 ≤ 24

5 0
2 years ago
Other questions:
  • What does it mean when there are variables on top of each other in parentheses in statistics?
    8·1 answer
  • In the standard (x,y) coordinate plane, what is the slope of the line 4x+7y=9?​
    8·1 answer
  • The Sun is roughly 10^2 times as wide as the Earth. The Star KW Sagittarii is roughly 10^5 times as wide as the Earth. About how
    12·1 answer
  • How many terms are in the expression 4(x + 8) + 5(y + 3) when simplified, and what are the terms?
    9·2 answers
  • Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 10
    6·1 answer
  • Wayne raked 30 bags of leaves in 3 hours.if he raked the same number of bags each hour,how many bags of leaves did he rake in on
    10·1 answer
  • Find the slope of the line that contains (2, -10) and (-4,2)
    5·1 answer
  • (someone help)
    15·1 answer
  • If triangle ACB is congruent to triangle DCE, angle CAB=50 degrees, angle DCE= 45 degrees, and angle CDE =10x what does x equal
    6·1 answer
  • Whats the answer to this?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!