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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.

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Answer:

10.8 gallons

Step-by-step explanation:

First change everything to inches:

2.75 ft = 33 in

1.5 ft = 18 in

Volume of tank = lwh = (33)(18)(7) = 4158 in³

The tank is 40% full, so only 60% is need to fill it. To find 60%, multiply 4158 by 0.6 = 2494.8 in³

Now find out how much 2494.8 in³ is in gallons:

231 in³ = 1 gallon

1 in³ = 1/231 gallons

2494.8 = (1/231)(2494.8) gallons = 10.8 gallons

Answer:

15 x 10 x 20 =

Step-by-step explanation:

Answer:

1,100

Step-by-step explanation:

15*10*2=300

20*15*2=600

20*10=200

300+600+200=1,100

you need to find the surface area which means the area of all the sides except the top(bc i think its open???)

a shortcut i used was multiplying sides that have the same area by 2. for example, the side 15*10, there was another side like that, so i multiplied by two instead of having to solve for the other side individually, does that make sense?

check my math if im wrong

Answer:

a) The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is 10.02.

Step-by-step explanation:

The t-distribution is used to solve this question:

a) n = 14

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7709

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) n = 28

27 df, T = 1.7033

[tex]M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88[/tex]

The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is

44 df, T = 1.6802

[tex]M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02[/tex]

The margin of error for a 90% confidence interval when n = 45 is 10.02.

Answer:

C

Step-by-step explanation:

400*.035 = 14 *2 = 28

250*.0325 = 8.125 *2 = 16.25

28 + 16.25  = 44.24

44.25+650 = 694.25

Answer:

Perpendicular

Step-by-step explanation:

Answer:

Perpendicular

Step-by-step explanation:

They form a 90 degree angle.

Answer:

16. 70%

17. 100%

Step-by-step explanation:

16. As seen here, there are 10 marbles in total. Out of those marbles, there are 7 green marbles.

We can set up a "part to whole" fraction such as 7/10

Then we just find the % value by finding an equivalent "x to 100" ratio (percentages go up to 100)

7/10 = x/100

1000 = 7x

70 = x

17. Fortunately, there doesn't seem to need too much math involved as the only possible marbles are red and green. Therefore, you have a 100% chance of getting a green or red marble.

Hope that helps a bit!

Answer:

pay for something and get money from ATM

Step-by-step explanation:

Answer:

area of right triangle = ab/2

                     base = 18yards

                    height = 2 1/3 = 7/3yards

area =  (18 * 7/3) /2 = 42 /2 = 21[tex]yards^{2}[/tex]

hope this answer helps you.....

Answer:

x>-2

Step-by-step explanation:

-8x+32-16<0

-8x<16

divide both sides by -8

x>-2

that's because when you divide by a negative your inequality sign changes

Answer:

4 for every dozen sold

Step-by-step explanation:

when the number of eggs sold is the dot at 12 on the x-axis, it is at 4 on the y-axis

Answer:

C

Step-by-step explanation:

What is the lowest common multiple

6 = 2 * 3

8 = 2 * 2 * 2

LCM = 2 * 2 * 2 * 3

LCM = 24

So you just divide 6 and 8 into 24. The result will be the number of packages.

Cups: 24/6 = 4

Plates: 24/8 = 3

You need 4 packs of cups and 3 of plates

Answer:

no por que 1/3 es menor que 4

Step-by-step explanation:

Answer:

95% of the lower confidence interval for the true average proportional limit stress of all such joints

7.7829

95% of the confidence interval for the true average proportional limit stress of all such joints

(7.7829, 9.3171)

Step-by-step explanation:

Step(i):-

Given that the sample size 'n' = 12

Mean of the sample = 8.55

The standard deviation of the sample (S) = 0.76

Step(ii):-

95% of the confidence interval is determined by

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom = n-1 = 12-1 = 11

t₀.₀₂₅ = 3.4966

[tex](8.55 - 3.4966\frac{0.76}{\sqrt{12} } , 8.55 + 3.4966 \frac{0.76}{\sqrt{12} })[/tex]

(8.55 - 0.7671 , 8.55+0.7671)

(7.7829, 9.3171)

Final answer:-

95% of the confidence interval for the true average proportional limit stress of all such joints

(7.7829, 9.3171)

Answer:

Anne

Step-by-step explanation:

Let's solve it by replacing x by 5, then -5.

(5+5)2=0

10*2=0

20=0

(-5+5)2=0

-5 and 5 cancel each other out, and 0 times anything is 0.

0=0

So Anne is correct.

--

hope it helps

Answer:

86 apples

Step-by-step explanation:

Hope this helps and have a great day!!!!

the nswer is 81 36/4=9

9x9=81

Answer:

isoceles and right

Step-by-step explanation:

Answer:

I think the answer us B........

Answer:

Step-by-step explanation:

The formula is P= a+b+c+d

a=base

b=base

c=side

d=side

Please search perimeter of a trapezoid.  It will provide the answer.

Answer:

Perimeter = 19.77 units

Step-by-step explanation:

Perimeter = AB + BC + CD + AD

BC = 5

AD = 8

AB² = 2² + 3² = 4 + 9 = 13

AB = √13 = 3.61

CD² = 1² + 3²  = 1 + 9 = 10

CD = √10 = 3.16

Perimeter = 3.61 + 5 + 3.16 + 8 = 19.77

Answer:400

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]7\tan \theta-\frac{7}{3}\cot \theta=0\\\tan \theta=\frac{1}{3} \cot \theta\\\tan^2\theta=\frac{1}{3}\\\tan \theta=\pm \frac{1}{\sqrt{3}}\\when ~\tan \theta=\frac{1}{\sqrt{3}}=tan 30,tan (180+30)\\\theta=30^\circ ,210^\circ\\when~ \tan \theta=-\frac{1}{\sqrt{3}}=\tan (180-30),tan(360-30)\\\theta=150^\circ,330^\circ[/tex]

solution set is {30,150,210,330}

Answer:

i am pretty sure it is 95

Step-by-step explanation:

Answer:

B IS THE ANSWER.

Step-by-step explanation:

The angle is less than 50 degrees but more than 30.

Answer:

so I just tried to find the mean (average) and it was: 6.3

Answer: 3:35

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sides of a quadrilateral always add up to 360°.

Missing angle = 360-115-97-68 = 80°

Answer:

D. 80°

Step-by-step explanation:

A quadrilateral always add up to 360°

To find the missing value we first have to add the given number up:

115 + 97 + 68 = 280°

Now we minus our value from 360° :

360° - 280° = 80°

Hope this helps!

Answer:

Ok.....

Step-by-step explanation:

Was that a question or was that the price you paid for getting a hair cut.

Answer:

Step-by-step explanation:

240 said apple juice and 340 said orange juice.

Answer:

The answer is 7

Step-by-step explanation:

2x+17+3x=4x+3x+3

5x+17=7x+3

5x-7x=3-17

-2x=-14

x=7