What is the minimum value of the objective function, C, with the given constraints?
C=2x+3y
A) 2x+3y≤24
B) 3x+y≤15
C) x≥2
D) y≥3
Answers
Given:
The objective function, [tex]C=2x+3y[/tex],
Constraints,
[tex]2x+3y\leq 24[/tex]
[tex]3x+y\leq 15[/tex]
[tex]x\geq 2[/tex]
[tex]y\geq 3[/tex]
To find:
The minimum value of the given objective function.
Solution:
We have,
Objective function, [tex]C=2x+3y[/tex] ....(i)
The related equations of given constraints are
[tex]2x+3y=24[/tex] ...(ii)
[tex]3x+y=15[/tex] ...(iii)
[tex]x=2[/tex], it is a vertical line parallel to y-axis and 2 units left from y-axis.
[tex]y=3[/tex], it is a horizontal line parallel to x-axis and 4 units above from y-axis.
Table of value for (i),
x : 0 12
y : 8 0
Table of value for (ii),
x : 0 5
y : 15 0
Plot these points on a coordinate plane and draw these 4 related lines.
The sign of inequality of [tex]2x+3y\leq 24[/tex] and [tex]3x+y\leq 15[/tex] is ≤, it means the related lines are solid lines and the shaded region lie below the related line.
For [tex]x\geq 2[/tex], left side of the line [tex]x=2[/tex] is shaded.
For [tex]y\geq 3[/tex], shaded region is above the line [tex]y=3[/tex].
From the below graph it is clear that the vertices of the feasible (common shaded region) are (2,3), (4,3), (3,6) and (2,6.667).
Points [tex]C=2x+3y[/tex]
(2,3) [tex]C=2(2)+3(3)=4+9=13[/tex] (Minimum)
(4,3) [tex]C=2(4)+3(3)=8+9=17[/tex]
(3,6) [tex]C=2(3)+3(6)=6+18=24[/tex]
(2,6.667) [tex]C=2(2)+3(6.667)=4+20=24[/tex]
Therefore, the objective function is minimum at point (2,3).
Related Questions
0.9b + 12 = 0.8b - 9
Answers
Answer:
0.9b+12=0.8b-9
0.9b+0.8b= -9-9
1.7b=-21
=-12.352
Find the present value of the given future payment at the specified interest rate.
6000$ due in 2 years at
6.5% compounded daily
Answers
Answer:
6.5% of 6000$=6000$x6.5/100=390$
amount of interest = 390$x2=780$
Compound Interest
n=1, 2
Po=6000$
Pn=Po(1+r)^n
Pn=6000$1+6.5%)^n
Pn=6000$(1.065)^n
P1=6000$(1.065)^1=6390$
P2=6000$(1.065)^2=6805.35
As an estimation we are told 5 miles is 8 km.
Convert 19.2 miles to km.
Answers
Answer:
about 30 km. If it wasn't estimated, it would be 30.8994048 km.
Answer:
12
Step-by-step explanation:
Tell whether the angles are complementary or supplementary. Then find the value of a
2x
(3x + 25)
Answers
Answer:
31
Step-by-step explanation:
3x + 25 + 2x = 180
3x + 2x = 180 - 25
5x = 155
x = 31
32+(-4) how i rezolv this
Answers
Answer:
=28
Step-by-step explanation:
Have a great day :)
Answer:
32 - 4 = 28
Step-by-step explanation:
just replace the plus sign since there is a negative
A right triangle has a base of 6m and a height of 8m. The slant (hypotenuse) is 10m. What is the DIFFERENCE Between the area of this triangle and the perimeter of this triangle?
Answers
Answer:
Step-by-step explanation:
Perimeter=a+b+c=6+8+10=24 m
Area=1/2*a*b=1/2*6*8=24 m^2
Do Now
A company has 3 locations with 70,010 employees altogether. The
first location has 34,857 employees. The second location has 17,595
employees. How many employees work in the third location?
Model
Answers
Answer:
17, 558 employees
Step-by-step explanation:
Altogether = 70,010 employees , First location = 34, 857 employees, second location = 17, 595 employees, Third location = ?
Let the number of employees in the third location be x
70,010 + 17, 595 + x = 70,010
x = 70, 010 - 52452
x = 17, 558( Answer)
17, 558 employees work in the third location
2x -6x2 -7 write the polynomial in standard form
Answers
Answer: It would be 2x-19
Step-by-step explanation:
convert 5/4 into a decimal
Answers
Answer:
Step-by-step explanation:
The answer is 1.25
Pls help need answers fast
Answers
Answer:
1. 11-y=-9
2. 41+w=26
3. r÷6=-4
4. 18(p)=54 or 18×p=54
5. Yes V= -52
6. Yes Z= -3
7. No would equal 43
8. No T would equal positive 6.
9. B
10. C
11. D
12. A
Can someone please help me on this? I've been trying for hours and can't seem to find the answer.
Answers
Answer: The area of the shape is 90 ft.
Step-by-step explanation:
Draw a line so the shape looks like a triangle and small rectangle.
First, we have to find the area of the rectangle.
Area of rectangle: length x width
The rectangle has a length of 6 ft and a width of 3 ft.
Area of rectangle: 6 x 3 = 18 ft
Now to find the area of the triangle.
Area of triangle: 1/2 x base x height
The triangle's base: 15 - 3 = 12
The triangle's height: 6 + 6 = 12
Area of the triangle: 1/2 x 12 x 12
= 1/2 x 144 = 72ft
To find the area of the entire shape you have to add the area of the rectangle and triangle together.
Area of shape = Area of rectangle + Area of triangle
A of shape = 18 ft + 72 ft
The area of the shape is 90 ft.
Hope that helped!
The product of the slopes of parallel lines is 1
Sometimes, never, or always
Answers
Answer:
Sometimes
Step-by-step explanation:
please help if u can! :))))
Answers
Answer: 0.8
Step-by-step explanation:
The formula to find area of a parallelogram is A = bh. This means that area = base x height. You can manipulate this formula to what height equals instead of the area. To do that, you can divide b on both sides. This would make the equation h = A/b.
Now that you know how to find what height equals, first find the base of the parallelogram. To find b, multiply 6 x 5. 6 x 5 = 30. This means that your base is 30.
Take the information given to you in the problem about the area. The area is given to you. We know that the area is 24 squared units. Remember what the equation to find height is. It's h = A/b. Substitute the variables for your numbers. h = 24/30.
24/30 = 0.8.
This means that your height is 0.8. This would be 8/10 in fraction form, but you can simplify it further to 4/5.
Hope it helps. Good luck!
A rectangular outdoor seating area has a length 5 feet greater than its width, w. Jonathan will increase both dimensions of the seating area by 3 feet. Which equation represents the new area, N, of the outdoor seating area?
Answers
which function has a y-intercept of 3
Answers
Answer:
2 and 3
1 also has a y-intercept of 3, but it is negative, so I don't know if that one will count
Step-by-step explanation:
Substitute X for 0 and solve from there.
3(0) - 2y = -6
0 - 2y = -6
y = 3
y - 3 = -2(0)
y - 3 = 0
y = 3
A park is rectangular with a length of 2/3 miles. If the area of the park is 3/9 square miles, what is its width? Input your answer as a fraction.
Answers
Answer:
6/9 miles
Step-by-step explanation:
I need help pls pls pls
Answers
Answer:
Mantle
Step-by-step explanation:
I think its mantle
If x=3y substitute the value of x into expression simplify 3x+6
Answers
Answer:
(3y)3+6
Step-by-step explanation:
Solve
for x
2(2x + 1) -10=4
Help please and thank you
Answers
Answer: 3
Distribute
Subtract the numbers
Simplify
How do you further solve this?
Answers
Answer:
x = ±√89-30 cos(55) (everything is under the radical)
and then plug the radical into a calculator and you get two answers:
x1= -9.39873
x2=9.39873
Step-by-step explanation:
i hope this helped :)
area of rhombus is 60m sq.if its perimeter is 40 m sq. find its altitude
Answers
Answer:
Step-by-step explanation:
Para meter of rhombus is equals 40 m
So one side of rhombus is equal to 10 m
Now
Area of rhombus is equals to half into base into altitude
1/2*10*altitude=84
Altitude = 16.8m
5c + d = c+ 4d find the ratio c:d
Answers
Answer:3c + 18d brainless pls
Step-by-step explanation:First, eliminate the parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
3
(
5
c
+
4
d
)
+
6
(
d
−
2
c
)
⇒
(
3
⋅
5
c
)
+
(
3
⋅
4
d
)
+
(
6
⋅
d
)
−
(
6
⋅
2
c
)
⇒
15
c
+
12
d
+
6
d
−
12
c
Next, group like terms:
15
c
−
12
c
+
12
d
+
6
d
Now, combine like terms:
(
15
−
12
)
c
+
(
12
+
6
)
d
3
c
+
18
d,
Given:
[tex]\to 5c + d = c+ 4d[/tex]
To find:
c:d=?
Solution:
\to 5c + d = c+ 4d
simulating the identical terms:
[tex]\to 5c -c = 4d-d\\\\\to 4c = 3d\\\\\to \frac{c}{d} = \frac{3}{4}\\\\\therefore\\\to c:d= 3:4[/tex]
so, the ratio is 3:4
Learn more about the ratio:
brainly.com/question/4534527
A bottie contains 255 coins.
1/3 of the coins are £1 coins.
110 of the coins are 50p coins.
The rest of the coins are 20p coins.
Work out the total value of the coins contained in the bottle.
Answers
Answer:
£152
Step-by-step explanation:
Solution:
Find out how much is 1/3 of 255 coins:
255 x 1/3 = 85
Since you know how many 50p and £1 coins there are, the remaining of the coins after the 50p and £1 get deducted from the total coins.
255 - 85 - 110 = 60
There are 60 20p coins, 85 £1 coins and 110 50p coins.
Find out the total value by calculating them all altogether.
60 x 20p = 1200
85 x 100p which is £1 = 8500
110 x 50p = 5500
I did them separately so that it wouldn't be so confusing.
Convert them into £, then after that add them up.
£12 + £85 + £55 = £152
Directions: Convert the following equations from standard form to slope-intercept form.
(10 points)
14. 4x + y = -1
15. 5x - 2y = 14
16. 10x - 2y = -6
17. 8x + y = 12
18. 6x - 10y = 20
Answers
y= 5/2x-7
y=5x+3
y= -8x +12
y= 3/5x-2
PLEASE HELP ASAP please someone help me so far my day has sucked and I need help. this is easy math just help meeeee.
5/6 +4/5
please help me answer correctly my grade depends on it
Answers
Answer:
1 19/30
Step-by-step explanation:
Answer:
NEVERMIND (I thought 45/30, but i dont know)
Step-by-step explanation:
What is the value of -b/(2a) in the given function below?
h(x)= -4x^2 -8x + 5
A. 2
B. -2
C. -1
D. 1
Answers
then we substitute the coefficients into the expression ➡️ x= -(-8/2x (-4)) and we solve the equation, so C (-1) is the correct answer!!
A diver is on a springboard that is 4 meters above the surface of the pool. another diver is 5 meters below the surface of the pool. Who is closer to the surface of the pool?
Answers
Answer:
A
Step-by-step explanation:
Let's say the surface of the pool is 0, and the diver 4 meters above represents +4, and the diver 5 meters below represents -5. Which number is closer to 0? It's 4! 4 is 4 numbers away from 0, meanwhile 5 is 5 numbers away from zero, 4 is closer to 0!
help please tell me if its a b c or d
Answers
Answer:
C
Step-by-step explanation:
just did it
Which number is the opposite of -3? Starting at -3, how many steps does it take to get to the opposite of -3? What does this number of steps represent?
Answers
Answer: 3 is the oppos ire of -3 and it takes 6 steps to get to it
Step-by-step explanation:
Answer:
"Which number is the opposite of -3?": The number that is opposite of (-3) is 3
"Starting at -3, how many steps does it take to get to the opposite of -3?": It takes 6 steps to get to the opposite of -3.
" What does this number of steps represent?": This number represents the distance between -3 and 3.
Step-by-step explanation:
Sammy has $180 in her savings account and plans to deposit $20 each month.
help me plz
Answers
Answer:
For a function f(x) = y.
The independent variable is the one that we chose to input in the function, in this case, is x, and the dependent variable is the variable that changes in response to the independent variable, in this case, is y.
In this problem we have:
"Sammy has $180 in her savings account and plans to deposit $20 each month."
We can define:
y = money in her savings account
x = number of months that have been passed since she started saving.
Originally, she has $180, and she saves $20 per month, so if x months have been passed, the total amount of money in her savings account is:
y = f(x) = $180 + $20*x
Now we want to know if this function is continuous or discrete, to see this we need to look at the possible values of x.
x represents the number of months that have been passed, then the values that x can take are:
x = 0, 1, 2, 3, 4, ...
So x can only take the values of positive integers, this means that the domain of x is discrete, then the function f(x) is a discrete function.
