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Answer:

Both prices should be set to #25.

The maximum revenue is #4375

Step-by-step explanation:

Given

[tex]q_1 = 150-2p_1-p_2[/tex]

[tex]q_2 = 200-p_1-3p_2[/tex]

Start by calculating the total revenue (R):

[tex]R = p_1q_1 + p_2q_2[/tex]

[tex]R = p_1(150-2p_1-p_2) + p_2(200-p_1-3p_2)[/tex]

[tex]R = 150p_1-2p_1^2-p_1p_2 + 200p_2-p_1p_2-3p_2^2[/tex]

Collect and solve like terms

[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]

Differentiate with respect to pi and to p2, respectively

[tex]\frac{dR}{dp_1} = 150 -4p_1 - 2p_2[/tex]

[tex]\frac{dR}{dp_2} = 200 -2p_1 - 6p_2[/tex]

Equate both to 0, to get the critical point

[tex]150 -4p_1 - 2p_2 = 0[/tex]

[tex]200 -2p_1 - 6p_2 = 0[/tex]

Solve for p1 in [tex]150 -4p_1 - 2p_2 = 0[/tex]

[tex]4p_1 = 150 - 2p_2[/tex]

[tex]p_1 = 37.5 - 0.5p_2[/tex]

Substitute [tex]p_1 = 37.5 - 0.5p_2[/tex] in [tex]200 -2p_1 - 6p_2 = 0[/tex]

[tex]200 - 2(37.5 - 0.5p_2) - 6p_2 = 0[/tex]

[tex]200 - 75 - p_2 - 6p_2 = 0[/tex]

[tex]125 - 7p_2 = 0[/tex]

[tex]-7p_2 =-125[/tex]

[tex]p_2 = 25[/tex]

Substitute [tex]p_2 = 25[/tex] in [tex]p_1 = 37.5 - 0.5p_2[/tex]

[tex]p_1 = 37.5 - 0.5 * 25[/tex]

[tex]p_1 = 37.5 - 12.5[/tex]

[tex]p_1 = 25[/tex]

So, we have:

[tex]p_1 = p_2 = 25[/tex]

This implies that the prices should be set to #25.

The maximum possible revenue is:

[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]

[tex]R = 150 * 25 + 200 * 25 -2 * 25^2 - 2 * 25 * 25 - 3 * 25^2[/tex]

[tex]R = 4375[/tex]

The maximum revenue is #4375

The maximum possible revenue is 4375.

From the information given, the following can be deduced:

Q₁ = 150 - 2P₁ - P₂

Q₁ = 150 - 2P₁ - P₂Q₂ = 200 - P₁ - 3P₂

The total revenue will be:

R = P₁Q₁+ P₂Q₂

R = P₁(150 - 2P₁ - P₂) + P₂(200 - P₁ - 3P₂)

R = 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²

To maximize, differentiate it in both the direction of P₁ and P₂.

d/dP₁ = 150 - 4P₁ - 2P₂

d/dP₂ = 200 - 2P₁ - 6P₂.

Solving for P₁ goes thus:

4P₁ = 150 - 2P₂

Divide through by 4

P₁ = 37.5 - 0.5P₂

Since 200 - 2P₁ - 6P₂ = 0

200 - 2(37.5 - 0.5P₂) - 6P₂ = 0.

P₂ = 25

Therefore, the revenue will be:

= 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²

= (150 × 25) + (200 × 25) - (2 × 25 × 25) - (3 × 25²)

= 4375

In conclusion, the revenue is 4375.

Learn more about revenue on:

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X   Y

1    8

2   11

3   14

4   17

5   20

6   23

7   26

8   29

9   32

10  35

11   38

12  41

13  44

14  47

15  50

16  53

17  56

18  59

19  62

20  65

Answer:

3/4

Step-by-step explanation:

Divide 3 3/4 by 5. 3 3/4 as an improper fraction is 15/4. 15/4 * 1/5 (divided by 5) is 3/4. :D dont report me

Answer:

A standard deck of cards consists of 52 cards. The colors are usually black for the spades and clubs and red for the hearts and diamonds.

Step-by-step explanation:

Answer:

There are 52 cards which are either red or black

Step-by-step explanation:

Answer:

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted.

This means that [tex]n = 80, \pi = \frac{44}{80} = 0.55[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.479[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.621[/tex]

The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).

Answer:  

70 + 2 + 0.3 + (-30) + (-9) + (-0.1) = 70 + (-30) + 2 + (-9) + 0.3 + (-0.1)  

Step-by-step explanation:  

i dont have an explanation but that is the answer i can confirm because i did it and got it wrong but then it showed the right answer hope it helps you

Answer:

25

Step-by-step explanation:

a=1/2bh

a=1/2(5)(10)

a=1/2(50)

a=25

Answer:

E

Step-by-step explanation:

Hope this helps the answer is 97!

Answer:

Step-by-step explanation:

4 6/7

Answer:

7√x = 14

Step-by-step explanation:

A radical equation is an equation in which a variable is under a radical. Out of all the equations, the only answer with x under the radical (square root symbol) is 7√x = 14.

The equation which is a radical equation from the given answer choices is; 7 √x = 14.

According to the task content;

On this note, the required equation is 7 √x = 14 because the variable is under a radical.

Read more on radical equation;

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Answer:

C.

Step-by-step explanation:

Trust me.

Answer:

the square root of 23 is 4.8 or if you need the longer one it's 4.79583152331

Answer:

z=529

Step-by-step explanation:

Let's solve your equation step-by-step.

√z=23

Solve Square Root.

√z=23

z=232(Square both sides)

z=529

Check answers. (Plug them in to make sure they work.)

z=529(Works in original equation)

Answer:

w=-[tex]\frac{3u}{2}[/tex]+2

Step-by-step explanation:

Answer:

w = -1.5u + 2

or

w = -3/2u + 2

Step-by-step explanation:

Your goal is to isolate w

-12u + 13 = 8w - 3

      +3             +3

-12u + 16 = 8w

 /8      /8    /8

-1.5u + 2 = w

w = -1.5u + 2

or

w = -3/2u + 2

Answer:

55

Step-by-step explanation:

60 minutes is an hour 60 - 5 is 55

Answer:

55

Step-by-step explanation:

60 minutes is an hour 60 - 5 is 55

Answer:

Your answer will be D. 15,840:) you're welcome, have a great day:)!

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{(25-7)(2)}{4}+2}[/tex]

[tex]\mathsf{25-7=\bf 18}[/tex]

[tex]\mathsf{\dfrac{\bold{18}(2)}{4}+2}[/tex]

[tex]\mathsf{18(2)= \bf 36}[/tex]

[tex]\mathsf{\dfrac{\bold{36}}{4}+2}[/tex]

[tex]\mathsf{\dfrac{36}{4}=\bf 9}[/tex]

[tex]\mathsf{\bold{9}+2 }[/tex]

[tex]\bold{= 11}[/tex]

[tex]\boxed{\large\textsf{Possible answer \#1: \bf 11 }}\huge\checkmark[/tex]

[tex]\huge\text{OR....}[/tex]

[tex]\mathsf{\dfrac{(25-7)(2)}{4+2}}[/tex]

[tex]\mathsf{25-7=\bf 18}[/tex]

[tex]\mathsf{\dfrac{\bold{18}(2)}{4+2}}[/tex]

[tex]\mathsf{18(2)=\bf 36}[/tex]

[tex]\mathsf{\dfrac{\bold{36}}{4+2}}[/tex]

[tex]\mathsf{4+2= \bf 6}[/tex]

[tex]\mathsf{\dfrac{36}{\bold{6}}}[/tex]

[tex]\mathsf{\bf = 6}[/tex]

[tex]\boxed{\large\textsf{Possible answer \# 2: \bf 6}}\huge\checkmark[/tex]

[tex]\boxed{\boxed{\large\text{{Answer(s): \bf Answer \#1: 11 OR Answer \#2: 6}}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Volume uses cubic ___  

A mile or kilometer is to big

So an cubic centimeter is about right

C

Answer:

exponent

Step-by-step explanation:

To get log2(4)=2

so 2 to the power of 2 is 4

4 is the number between brackets in log

another example

log2(8)=3

2 to the power of 3 is 8

Answer:

67

Step-by-step explanation:

complementary mean it equals 90 degrees

90-23 = 67

m<2=67

Answer:

rational i just know it hope it helps you

Answer:

Rational

∛-8

=-2

plz mark me as brainliest.

Answer:

The limit does not exist

Step-by-step explanation:

The first step would be to try to evaluate the functions at x = 0

5x - 9 => 5(0) - 9 = -9

| 2 - x | => | 2 - 0 | = 2

So they can be evaluated at x = 0, and it gives two different answers so the limit does not exist

Answer:

The limit does not exist

Step-by-step explanation:

By evaluating both functions we see that we get -9 and 2, because they are not equal to each other the limit does not exist.

Answer256pi

Step-by-step explanation:

Area=pi*r^2

=pi*16^2

256pi

Its not yet known. We need other numbers and letters!

Answer:

JKM is 123 degrees and the measure of arc KL is 56

Answer:

she swam 63 minutes more than in the first

Step-by-step explanation:

first week only = 142 minutes

total week = 347

second week only = 347 - 142 = 205 minutes

205 - 142 = 63 minutes

Answer:

(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2

(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2

(with pi rounded to 3.14) = 94.25 in^2

Step-by-step explanation:

Let's start with the easier shape, the triangle. The formula for area of a triangle is 1/2(base)(height). Since at the far right we have 10 in, we can apply that to the triangle to get the base = 10 inches. The height is given as 11 inches so we can then calculate the area which is 55 in^2.

Then, the circle. We know that area of a whole circle = [tex]\pi r^{2}[/tex]. Since we know that a semicircle is 1/2 of a full circle, we can find the area of the entire circle then divide it by 2.

It gives the diameter as 10, divide that by 2 to get the radius. r=5. Plug 5 into the equation of [tex]\pi r^{2}[/tex] and you get 25[tex]\pi[/tex]. Divide that by 2 to get 25[tex]\pi[/tex]/2.

Add the triangle and the semicircle areas.

(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2

(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2

(with pi rounded to 3.14) = 94.25 in^2

Answer:

Initial Deposit= $800

Annual rate= .1%

Leaves= 8 years

8 x .1= .8

$800 x .8= $640

$800+$640= $1,440

So your answer is $1,440 is the bank balance in 8 years

Step-by-step explanation:

hope i help have a great day

Answer:

30% man this easy

Step-by-step explanation:

PLS GIMME BRAINLIEST PLS