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
Artemon [7]
3 years ago
6

Solve the linear programming problem. Minimize and maximize Upper P equals negative 20 x plus 30 y Subject to 2 x plus 3 y great

er than or equals 30 2 x plus y less than or equals 26 negative 2 x plus 3 y less than or equals 30 x comma y greater than or equals 0

Mathematics
1 answer:
Alika [10]3 years ago
7 0

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

2x+3y\ge 30            .... (1)

2x+y\le 26            .... (2)

-2x+3y\le 30            .... (3)

x,y\geq 0

The related equation of given inequalities are

2x+3y=30

2x+y=26

-2x+3y=30

Table of values are:

For inequality (1).

x      y

0     10

15     0

For inequality (2).

x      y

0     26

13     0

For inequality (3).

x      y

0     10

15     0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

2(0)+3(0)\ge 30\Rightarrow 0\ge 30    False

2(0)+(0)\le 26\Rightarrow 0\le 26     True

-2(0)+3(0)\le 30\Rightarrow 0\le 30    True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point           P = 20x + 30y

(0,10)           P = 20(0) + 30(10) = 300

(6,14)           P = 20(6) + 30(14) = 540

(12,2)           P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

You might be interested in
What scale factor was applied to the first rectangle to get the resulting image?
madam [21]

Answer:

The scale factor for the resultant rectangle is\frac{2}{5} units.

Step-by-step explanation:

Given two rectangles with sides 3 units and 7.5 units.

We have to find the scaling factors so that we can obtain bigger rectangle of 7.5 units from smaller rectangle of 3 units.

Scale factor is defined as the ratio  of corresponding side of given figure to the corresponding side of resulting figure.

That is \text{Scale factor}=\frac{\text{length of side of given figure}}{\text{length of side of resulting figure}}

Here, \text{Scale factor}=\frac{\text{length of side of given rectangle }}{\text{length of side of resulting rectangle}}

\text{Scale factor}=\frac{3}{7.5}=\frac{2}{5}

Hence, the scale factor for the resultant rectangle is\frac{2}{5} units.  

4 0
3 years ago
6, 3, 4, 7, 3, 7, 8, 5, 7 i. Find the median ii. Find the mean iii. Find the modal mark
4vir4ik [10]

Answer:

i. 6

ii. 5\frac{5}{9}

iii. 7

Step-by-step explanation:

First organize the data from least to greatest.  3,3,4,5,6,7,7,7,8

To find the median, remove the extremes from the data over and over.

3,4,5,6,7,7,7

4,5,6,7,7

5,6,7

6

To find the mean, add all of the numbers and divide by 9

3+3+4+5+6+7+7+7+8=50

50/9=5\frac{5}{9}

To find the modal mark, simply find the number present most in the data set: 7(occurs 3 times)

Hope it helps <3

3 0
3 years ago
Hi, I have a Q, how do I use it?
anygoal [31]

Answer:

use what

Step-by-step explanation:

3 0
2 years ago
Kate and Jean paint a house together in 6 days. If they work alone, Kate takes 5 fewer days than Jean would take to do the same
navik [9.2K]
X = number of days it would take Kate to paint the house by herself. .
<span>x+5 = number of days it would take Jean to paint the house by herself.</span>
<span>Together, they paint the house in 6 days: </span>
<span>1/x + 1/(x+5) = 1/6 </span>
<span>Multiply both sides by 6x(x+5) </span>
<span>6(x+5) + 6x = x(x+5) </span>
<span>12x + 30 = x^2 + 5x </span>
<span>x^2 − 7x − 30 = 0 
</span>therefore the answer is A.

4 0
3 years ago
Read 2 more answers
Find the value of x in the following figure ( Please hurry)
kolbaska11 [484]

Answer:

x=9

Step-by-step explanation:

2x+12=5x-15

3x=27

x=9

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is 8 4/7 divided by 15 equal
    13·2 answers
  • HELPPP
    5·1 answer
  • Tuition of $
    7·1 answer
  • If james has 2 pieces of candy and gives 2 away but john gives him 2 more how much candy does james have?
    15·2 answers
  • 1) In triangle ABC, LC = 90, Write Pythagoras theorem for triangle.​
    5·1 answer
  • If i earn 165 dollars in 20 hours how many would i make in 40 hourr
    15·1 answer
  • Plssss HELP MEEEEEE<br> i shall give thanks
    13·2 answers
  • Find the time it takes an object to hit the ground when it is dropped from:
    9·1 answer
  • Tell me where to plot it please!
    7·1 answer
  • Solve for x using the circle below. Enter the value of x rounded to the nearest wholenumber.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!