What is the constant rate???

Answer:

a. The number of units which will minimize average cost is approximately 5,130 units.

b. The firm should produce 12,500 items, x, for maximum profit.

c. The number of items, x, that will produce a maximum profit is 60 items.

Step-by-step explanation:

Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

The explanation to the answer is now given as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

Given;

C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)

We first simplify (0.02x + 6)^3 as follows:

(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)

First, we have:

(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36

Second, we have:

(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216

Therefore, we have:

C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)

C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200

Therefore, the average cost (AC) can be calculated as follows:

AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x

AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)

AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)

Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:

0.032x + 10.08 - (43,300 / x^2) = 0

0.032x + 10.08 = 43,300 / x^2

X^2 * 0.32x = 43,300 – 10.08

0.32x^3 = 43,189.92

x^3 = 43,189.92 / 0.32

x^3 = 134,968.50

x = 134,968.50^(1/3)

x = 51.30

Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:

x = 51.30 * 100 = 5,130

Therefore, the number of units which will minimize average cost is approximately 5,130 units.

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

P(x) = R(x) - C(x) ……………. (3)

Where;

P(x) = Profit = ?

R(x) = 450x-1/100x^2

C(x) = 500 + 200x

Substituting the equations into equation (3), we have:

P(x) = 450x - 1/100x^2 - (500 + 200x)

P(x) = 450x - 0.01x^2 - 500 - 200x

P(x) = 450x - 200x - 0.01x^2 - 500

P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)

Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:

250 - 0.02x = 0

250 = 0.02x

x = 250 / 0.02

x = 12,500 items

Therefore, the firm should produce 12,500 items, x, for maximum profit.

3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

Given;

P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)

Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:

3600 + 120x - 3x^2 = 0

Divide through by 3, we have:

1200 + 40x – x^2 = 0

1200 + 60x – 20x – x^2 = 0

60(20 + x) – x(20 + x) = 0

(60 – x)(20 + x) = 0

Therefore,

x = 60, or x = - 20

The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.

Answer:

27

Step-by-step explanation:

Since 9 is the amount of lollipop Molly has and her friend has 3 times more; which is 9x3

Answer:

-48 there is a pattern

Answer:

a

Step-by-step explanation:

Answer:

look below for question

Step-by-step explanation:

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3  

Only values that satisfy y > 3x + 1 are solutions.

Only values that satisfy y < 3x – 3 are solutions.

Values that satisfy either y > 3x + 1 or y < 3x – 3  are solutions.

There are no solutions.

Answer:

hehdhrhth

Step-by-step explanation:

thrhrgefwy3ihrgej eff wr3 utf egtje creek it g

Answer:

f(5.6) = 2.6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = [x - 3]

f(5.6) is x = 5.6

Step 2: Evaluate

Answer:

15

Step-by-step explanation:

3 × 5 = 15

Hope this helped <3

Answer:

The distance between the hands is √(3)cm ≈ 1.73cm.

Step-by-step explanation:

In a standard clock, the angle between every number is 30°, therefore the angle between 12 and 2 will be 30° x 2 = 60°.

Looking at the diagram, to find c we can make use of our cosine formula

c² = a² + b² –2abCos(C°)

a = 2, b = 1 and C° = 60°

Therefore we have:

c² = 2² + 1² –2 x 2 x 1 x cos(60°) =

c² = 4 + 1 – 4 x 0.5 =

c² = 5 – 2 =

c² = 3

c = √(3) ≈ 1.73

Therefore, the distance between the hands is √(3)cm ≈ 1.73cm.

Answer:

3

Step-by-step explanation:

To give the same amount of stamps to each student you would divide 67 by 8. Dividing would give each students 8 stamps because you can only equally divide it to 64 (EX, 64/8=8). This leaves you with 3 stamps leftover, because we only used 64 equally and 67-64=3.

Answer:

He can give each of his students 8 stamps.

With 3 stamps left over.

Step-by-step explanation:

Hope this helps!

See attachment for math work and answer.

Answer:

1.5 goes in between the 0 and the first line (meaning 1) and 0.5 goes in between the left of the zero and the line before the zero

Answer:

1.3

Step-by-step explanation:

8 divided by 6 = 1.3

BRAINLIEST PLEASE

Answer:

1.3

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

C

Step-by-step explanation:

Answer:

thank you

Step-by-step explanation:

Answer:

yes it's easy

Step-by-step explanation:

y=-2x

it may help you to understand.

Answer:

the answer is A 90+0.25x=147.50

Step-by-step explanation:

if this is useful please make me brainliest

Answer:

Part a: 7.5

Part B: It changes by 1.5

Step-by-step explanation:

PART A:

In the table you are suppose to find out how much it increases by so you subtract,

[tex]4.5 - 3 = 1.5[/tex]

[tex]6 - 4.5 = 1.5[/tex]

Since we know the difference is 1.5 you will add 6 by 1.5

[tex]6 + 1.5 = 7.5[/tex]

Therefore, the answer is 7.5

PART B: It changes by 1.5 because the difference between the increase in points is 1.5

Answer:

#2) 30% of 400 is 120 and 120/6 = 2 so it took him 2 hours

#3) 2.5/3.2 = .78 and 1/1.2 =.83 so buying the bigger one you are paying less

Answer: 105

Step-by-step explanation:

Answer:

34.28 percent of the items in the bag are DVDs

Step-by-step explanation:

Given that he had following items

DVDs 12

MArbles 12

Books 11

Total items are: 11+12+12 = 35

In order to find the percentage of DVDs we have to divide the quantity of DVDs by total and multiply by 100

So,

Percentage of DVDs is:

[tex]=\frac{12}{35} *100\\= 0.3428*100\\= 34.28\%[/tex]

Hence,

34.28 percent of the items in the bag are DVDs

Answer:

If he missed five questions he can get a zero

Step-by-step explanation:

Answer:

3 cm on the map represents 31.5 km in reality.

3cm : 31.5 km

1cm :  31.5/3 km

1cm : 10.5km

So the scale on the map is 1cm represents 10.5 km.