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
(x,-4) and (2,8): m = -3 find the missing value. it is in slope formula.
Snezhnost [94]

Answer:

The value of x = 6

Step-by-step explanation:

Given

  • The point (x,-4)
  • The point (2,8)

To determine

  • m = -3

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

here:

  • (x₁, y₁) = (x, -4)
  • (x₂, y₂) = (2, 8)
  • m = -3

so substitute (x₁, y₁) = (x, -4) , (x₂, y₂) = (2, 8)  and m = -3

m =  [y₂ - y₁] /  [x₂ - x₁]

-3 =  [8 - (-4)] / [2 - x]

-3 = [12] / [2-x]  

-3 (2-x) = 12

-6+3x = 12

3x = 12+6

3x = 18

divide  both sides by 3

3x/3 = 18/3

x = 6

Therefore, the value of x = 6

7 0
3 years ago
Diego made a scale drawing of a theater. The scale of the drawing was 1 inch : 3 feet. The
Artyom0805 [142]

Answer:

The actual stage is 42 feet long

Step-by-step explanation:

Step 1

Determine the conversion factor as shown;

1 inch in the drawing represents 3 feet in the actual drawing

To convert a measurement in inches in the drawing to an actual measurement, we use a conversion factor of 3. In the same way, to convert a measurement in feet in the actual stage to the drawing measurement in inches, we use a conversion factor of (1/3).

Step 2

Convert 14 inches in the drawing to the actual measurement of the stage as follows;

Actual stage length=drawing length×conversion factor

where;

drawing length=14 inches

conversion factor=3

replacing;

Actual stage length=(14×3)=42 feet

The actual stage is 42 feet long

3 0
2 years ago
You are constructing triangle ABC given the line segments AB and AC and ∠A. The first thing you do is copy segment AC. Next, you
nikitadnepr [17]

Answer:

copy AB



Step-by-step explanation:


7 0
2 years ago
Read 2 more answers
Find the value of the given variable (-4, r) (-8, 3) m=5
UNO [17]
R=23 because its slope the formula is Y-Y/X-X


6 0
3 years ago
Write in exponent form 85
Nataly [62]

We are given 85

Firstly, we will find all possible factors of 85

we can write it as

85=1*5*17

so, exponential form is

85=5^1*17^1................Answer

4 0
3 years ago
Other questions:
  • Laminate buys 12 packs of juice and pays a total of $48. Use a ratio table to determine how much she will pay to buy 8 more pack
    12·1 answer
  • Solve the given system, using the substitution method.
    13·1 answer
  • Ryan has an eight-year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually. Calculate the to
    11·1 answer
  • Five less than thw product of 3 and a number is 8
    11·1 answer
  • What 42 rounded to the nearest ten​
    12·1 answer
  • Find the value or x. <br> -<br> a. 5 <br> b. 11<br> c. 25<br> d. 31
    7·1 answer
  • Gretta is saving for retirement. She deposits $125 each month at 6% annual interest for 35 years. According to her calculations,
    7·1 answer
  • Solve equation 2x/4+1/3=X/6 needed urgently please right now​
    14·1 answer
  • The sum of three consecutive even integers is −246. Find the three integers.
    9·1 answer
  • I need help,<br> Find the perimeter of the rectangle. Write your answer in Scientific Notation
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!