MATHEMATICS HIGH SCHOOL

Using the following system of inequalities find the maximum value of f(x,y) = 3x + 7yx≥0
y≥0
3x+2y≤18
6x+7y≤42

Answer:

Answers

Answer 1
Answer: x ≥ 0
y ≥ 0
f(x, y) = 3x + 7y
f(0, 0) = 3(0) + 7(0)
f(0, 0) = 0 + 0
f(0, 0) = 0

3x + 2y ≤ 18 ⇒ 3x + 2y = 18 ⇒ 21x + 14y = 126
6x + 7y ≤ 42 ⇒ 6x + 7y = 42 ⇒ 12x + 14y =   84
                                                              9x = 42
                                                               9      9
                                                                x = 4²/₃
                                                      3x + 2y = 18
                                                3(4²/₃) + 2y = 18
                                                      14 + 2y = 18
                                                    - 14         - 14
                                                              2y = 4
                                                               2     2
                                                                y = 2
                                                          (x, y) = (4²/₃, 2)
f(x, y) = 3x + 7y
f(4²/₃, 2) = 3(4²/₃) + 7(2)
f(4²/₃, 2) = 14 + 9
f(4²/₃, 2) = 23

Related Questions

Evaluate the expression: -6 - |3 - 7| × 4 ÷ 8 - (-2) =
What is the next letter? Y B W D U F
The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds. How far does the elevator travel in 12 seconds?
You went out for dinner with your family. The bill was $160 and your family left a20% tip. How much was the tip? How much was the total?
A coffee shop mixes Brazilian coffee worth $5 per kilogram with Turkish coffee worth $8 per kilogram. The mixture is to sell for $7 per kilogram. How much of the Turkish coffee should be used to make 300 kg of the mixture?

33 1/3 percent of 600

Answers

33(1)/(3)×(1)/(100)=(1)/(3)
To change percent to fraction/decimal
(1)/(3)×600=200
Answer: 200
331/3 of 600 331/3×600 100/3×1/600. 1/12×100 =81/3%

What is bigger 10 pounds or 10 kilograms

Answers

10 kilograms are bigger. 
None are bigger than the other since they are both weight measures and not size measures. If you were asking which is heavier than your answer is 10 kilograms.

A calculator was purchased for $29. The wholesale cost was $20. What was the percent markup?

Answers

If you would like to find the percent markup, you can calculate this using the following steps:

x% of $20 is $29
x% * 20 = 29
x/100 * 20 = 29
x = 29 * 100 / 20
x = 145%

145% - 100% = 45%

The correct result would be 45%.

What is the 52nd number of pi?

Answers

5 is the 52nd number in pi

Which is a true statement about an exterior angle of a triangle

Answers

The true statement about an exterior angle of a triangle is C; It forms a linear pair with one of the interiior angles of the triangle .

What is the Exterior Angle of a Triangle Property?

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

We know that the exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.

The pair also rests on the same straight line and that makes a pairs.

Therefore we can say that it is formed by a linear pair with one of the interior angles of the triangle.

So, the correct answer would be C.

Learn more about exterior angles;

brainly.com/question/14164971

#SPJ2

Answer:

D

Step-by-step explanation:

The exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.

The pair also rests on the same flat/straight line and that makes a pair.

Therefore we can say that it is formed by a linear pair/group with one of the interior/inside angles of the triangle.

So, the correct answer would be D.

How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

Answers

LHS\n \n =\frac { \tan ^( 2 ){ x-\sin ^( 2 ){ x } } }{ \tan { x } } \n \n =\frac { 1 }{ \tan { x } } \left( \tan ^( 2 ){ x-\sin ^( 2 ){ x } } \right)

\n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x } }{ \cos ^( 2 ){ x } } -\frac { \sin ^( 2 ){ x\cos ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \right) \n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x-\sin ^( 2 ){ x\cos ^( 2 ){ x } } } }{ \cos ^( 2 ){ x } } \right)

\n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\left( 1-\cos ^( 2 ){ x } \right) } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\cdot \sin ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } \sin ^( 4 ){ x } }{ \sin { x\cos ^( 2 ){ x } } } \n \n =\frac { \sin ^( 3 ){ x } }{ \cos { x } }

\n \n =\sin ^( 2 ){ x } \cdot \frac { \sin { x } }{ \cos { x } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \cot { x } } \n \n =\frac { \sin ^( 2 ){ x } }{ \cot { x } } \n \n =RHS
Other Questions
How could you use the product of 108 and 4 find the product of 324 and 4
Number line from negative 10 to 10 , tic marks at every integer , labels at negative 10 , negative 5 , 0 , 5 , 10 , closed red circle on negative 1 , red shading to the right of the red circle. A. y + 5 ≤ 4 B. y + 5 < 4 C. y + 5 ≥ 4 D. y + 5 > 4
Twenty divided by 60
Which is the side length of a cube with a volume of 64 m3?