MATHEMATICS COLLEGE

A company’s total cost from manufacturing and selling x units of their product is given by: y = 2x2 – 600x + 49,000. How many units should be manufactured in order to minimize cost, and what is the minimum cost?a. (100, $9,000)b. (125, $3,250)c. (150, $4,000)d. (170, $4,800)e. (200, $9,000)

Answers

Answer 1

Answer:

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

$y=2x^2-600x+49000$

We need to find the number of units in order to minimize cost.

We first derivative w.r.t. x,

$y'=4x-600$

For critical points:

$y'=0\n\n4x-600=0\n\n4x=600\n\nx=(600)/(4)\n\nx=150$

Now, we will check whether it is minimum or not.

We will find second derivative .

$y''=4>0$

So, it will yield minimum cost.

Minimum cost would be

$y(150)=2(150)^2-600* 150+49000\n\ny(150)=\$4000$

Hence, At 150 units, minimum cost = $4000

Therefore, Option 'c' is correct.

Related Questions

What number Could be added in the expression -4 -9 that the value of the expression is 0
Adam is climbing up the stairs in a building. At a certain point, Adam starts counting the steps and when he reaches the last step, he has counted 56 steps. If he knows that there are a total of 100 steps in the building, how many steps did he climb before he started counting the steps?
Which words in the salutation should be capitalized? dear aunt mary, Choose all answers that are correct.A.MaryB.DearC.Aunt
I AM IN A TEST AND I NEED THE ANSWER SOON!!! PLEASEE!!!THANK YOU SO MUCH!!
7. Given a right triangle as shown below, use a calculator to estimate the length of themissing side to the nearest tenth of a centimeter

If x=2 find y 5x-y=5

Answers

Answer:

y=5

solution,

X=2

now,

$\n 5x - y = 5 \n or \: 5 * x - y = 5 \n or \: 5 * 2 - y = 5 \n or \: 10 - y = 5 \n or \: - y = 5 - 10 \nor \: - y = - 5 \n y = 5$

hopethishelps..

Goodluck on your assignment..

Hot air balloons are able to fly at a very high altitudes a world record height of 64997 feet was set in 1988 in 2005 a new record of 68986 feet was set how many feet higher was 2005 record than the 1988 récord first draw a diagram to show the parts of the problem

Answers

Answer:

just do 68986

- 64997

______

3,989

Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.

Answers

Answer:

Speed of a= 21 miles/hr

r = Speed of b= 7 miles/hr

Speed of a = 3r

Step-by-step explanation:

The cyclist are 112 miles apart

Time traveled by two = 4 hours

Speed of a = 3 * speed of b

If a cylcles 3 times More than b, then a will cover 3*distance of b

But speed = distance/time

Time = 4hours

Total distance=112

a = 3b

3b + b = 112

4b = 112

b = 112/4

b = 28 miles

a = 3b

a = 3*28

a = 84 Miles

They bought traveled 4 hours

Speed of a = 84miles/4 hours

Speed of a= 21 miles/hr

Speed of b = 28miles/4 hours

Speed of b = 7 miles/hr

Final answer:

The slower cyclist is traveling at a speed of 7 mph, while the faster cyclist is traveling at 21 mph.

Explanation:

We first need to recognize that the sum of the distances travelled by each cyclist is equal to the total 112 miles. We can let r represent the speed of the slower cyclist, and since the faster cyclist is traveling 3 times the speed of the slower, we can call his speed 3r.

As they each traveled for 4 hours, the slower cyclist traveled a distance of 4r miles, and the faster cyclist traveled a distance of 4 × 3r = 12r miles. Their combined distances should equal the total distance between them, 112 miles. This forms the equation 4r + 12r = 112.

To solve for r, we combine the like terms on the left side of the equation to get 16r = 112. Dividing both sides by 16, we find r = 7 miles per hour. Therefore, the slower cyclist is traveling at 7 mph, and the faster cyclist is traveling 3 times that speed, giving us 21 mph.

Learn more about Speed here:

brainly.com/question/22610586

#SPJ3

Let S = {a, b, c). Find the following:a) the number of reflexive relations on S

b)the number of reflexive and symmetric relations on S

Answers

Answer:

The number of reflexive relations on S is 64.

The number of reflexive and symmetric relations on S is 8.

Step-by-step explanation:

Consider the provided set S = {a, b, c}.

The number of elements in the provided set is 3.

Part (a) the number of reflexive relations on S

To calculate the number of reflexive relation on S we can use the formula as shown:

Total number of Reflexive Relations on a set: $2^(n(n-1))$ .

Where, n is the number of elements.

In the provided set we have 3 elements, so substitute the value of n in the above formula:

$2^(3(3-1))$

$2^(3(2))$

$2^(6)$

$64$

Hence, the number of reflexive relations on S is 64.

Part(b) The number of reflexive and symmetric relations on S.

To calculate the number of reflexive and symmetric relation on S we can use the formula as shown:

Total number of Reflexive and symmetric Relations on a set: $2^{(n(n-1))/(2)}$ .

Where, n is the number of elements.

In the provided set we have 3 elements, so substitute the value of n in the above formula:

$2^{(3(3-1))/(2)}$

$2^{(3(2))/(2)}$

$2^{(6)/(2)}$

$2^(3)$

$8$

Hence, the number of reflexive and symmetric relations on S is 8.

I’m very confused pls help 50 PTSFind the quadratic function y=ax^2 +bx+c whose graph passes through the given points. (-1,-11) (2,-26) (-3,-31)

Answers

The quadratic value function is y = -x² - 4x + 16

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

Let the function passes through the given points. (-1,-11) (2,-26) (-3,-31)

And , using the point (-1,-11) , we get

-11 = a(-1)² + b(-1) + c

-11 = a - b + c

Using the point (2,-26) , we get

-26 = a(2)² + b(2) + c

-26 = 4a + 2b + c

Using the point (-3,-31) , we get

-31 = a(-3)² + b(-3) + c

-31 = 9a - 3b + c

And , the three set of equations are

-11 = a - b + c

-26 = 4a + 2b + c

-31 = 9a - 3b + c

From the first equation, we can solve for c:

c = 11 - a + b

Substituting this expression for c into the other two equations, we get:

-26 = 4a + 2b + 11 - a + b

-31 = 9a - 3b + 11 - a + b

Simplifying these equations, we get:

-15 = 3a + 3b

-21 = 8a - 2b

Solving the first equation for b in terms of a, we get:

b = -5 - a

Substituting this expression for b into the second equation, we get:

-21 = 8a - 2(-5 - a)

Simplifying and solving for a, we get:

a = -1

Substituting this value of a into the equation for b that we found earlier, we get:

b = -5 - (-1) = -4

Finally, substituting these values of a and b into the equation for c that we found earlier, we get:

c = 11 - (-1) - (-4) = 16

Hence , the quadratic function that passes through the given points is given by y = -x² - 4x + 16

To learn more about quadratic equations click :

brainly.com/question/25652857

#SPJ1

1) How do you describe Ana in the selection?

Answers

Answer:

she develops a fair and healthy relationship with her classmate but also she elected the class president at their school

Step-by-step explanation:

vote me as the brainliest

Other Questions

Pls help me someone this is annoying me

If minor arc AB measures 9 inches, what is the length of the radius of circle C?

Change 11/5 from an improper fraction to a mixed number

Part A: Factor x2b2 − xb2 − 6b2. Show your work. Part B: Factor x2 + 4x + 4. Show your work.Part C: Factor x2 − 4. Show your work