Answer:
a) x = 798 is the quantity that maximizes the profit
b)po(x) = 401 $/unit
c)P(max ) = 636105 $
Step-by-step explanation:
The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:
R(x) = p(x) * x
R(x) = ( 800 - 0,5*x ) * x
R(x) = 800*x - 0,5*x²
The equation for the profit is:
P(x) = R(x) - C(x)
P(x) = 800*x - 0,5*x² - ( 300 + 2*x)
P(x) = 798*x - 0,5*x² - 300
a) P(x) = 798*x - 0,5*x² - 300
Taking derivatives on both sides of the equation:
P´(x) = 798 - x
If P´(x) = 0 then 798 - x = 0
x = 798 is the quantity that maximizes the profit
b) Selling price for the optimal quantity is:
p(x) = 800 - 0,5*x
p(x) = 800 - 0,5* 798
po (x) = 800 - 399
po(x) = 401 $/unit
c) Pmax = ?
P(x) = 798*x - 0,5*x² - 300 by subtitution of x = 798
P(max) = 636804 - 399 - 300
P(max ) = 636105 $
a) The quantity that will maximize profit is [tex]100 \ units[/tex].
b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.
c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].
Demand Function:A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.
The given demand function,
[tex]P=800-\frac{1}{2}x[/tex]
So, the revenue function is,
[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]
[tex]\Rightarrow[/tex]Average cost is
[tex]\bar{C}=300+2x[/tex]
So, the total cost function is,
[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]
a) Profit function:
[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]
For maximum,
[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]
b) Selling Price:
[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]
c) Maximum Profit:
[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]
Learn more about of Demand Function: https://brainly.com/question/25938253
What is the value of a in the proportion???? need help!!!
Answer:
90
Step-by-step explanation:
90-15/90= 5/6
90-15= 75
75/90= 83.3333 or 5/6
Jillian is at her favorite clothing store and has found a pair of pants that are on sale for 20% off the regular price. They
are regularly $28. How much will be taken off the price?
$4,60
$8.00
$6.00
$5.60
Answer:
5.60 it answer D hope it helps ~••~
Please answer this correctly without making mistakes
Answer: 96%
1 square represent 1%
Answer:
96 present
Step-by-step explanation:
100 POINTS SHOW YOUR WORK, ANSWER ALL PLEASE HELP!!!!
A chef has a favorite muffin recipe that uses 1/2 cup of blueberries for a whole batch. He has 3/4 cups of blueberries that he wants to use. Which equation can be used to solve for the number of batches of muffins, b, that the chef can make?
3/4 ÷ 1/2 = B
3/4 ÷ 2/1 = B
1/2 ÷ 3/4 = B
2/1 ÷ 3/4 = B
Monty has 3/4 pound of trail mix. He needs to divide the trail mix into 1/8 pound bags. How many trail mix bags will Monty have?
An adult elephant in the wild spends about 16 hours each day eating. During that time, the elephant will eat about 525 pounds of food.
If the elephant eats the same amount of food each hour, about how much food does it eat in one hour, to the nearest whole pound? Show or explain how you got your answer.
Members of the school orchestra are organizing a trip to a concert. If tickets cost $14 each, how many tickets can be purchased with $500?
Mr. Morris used the greatest common factor and the distributive property to rewrite the sum 45 + 27.
What did he write?
A club with 24 members has 4,896 event flyers to pass out.
Each member will be given the same number of flyers.
How many flyers does each member get?
Xavier is solving a problem on the whiteboard as shown.
Part A. Is Xavier's solution correct? If not, identify where he made an error.
Part B. Solve 7950 divided by 25.
Quantity of trail mix with Monty = 3/4 pounds
Quantity of pounds he need to divide it into = 1/8
Number of trail mix bags Monty will have =
= 3/4 ÷ 1/8
= 3/4 × 8/1 ( division of fraction is multiplication with reciprocal )
= 24/4
We know that both 24 and 4 is divisible by 4 . Hence ,
= 24 ÷ 4 / 4 ÷ 4
= 6/1
= 6 bags
Therefore , Monty will have 6 bags of trail mix .
Solution 3 :Quantity of food an elephant eats in 16 hours = 525 pounds
Quantity of food the elephant will eat in 1 hour = 525 ÷ 16
Quantity of food the elephant will eat in 1 hour = 32.8125 pounds = 33 pounds
Therefore , an elephant eats 33 pounds of food in 1 hour .
Solution 4 :Number of tickets that can be purchased with $14 = 1 ticket
Number of tickets that can be purchased with $500 =
= 500 ÷ 14
= 35 tickets
Therefore , 35 tickets can be purchased with $500 .
Solution 5 :Factors of 45 = 1 , 5 , 3, 9 , 15 and 45 .
Factors of 27 = 1 , 3 , 9 and 27 .
Their Greatest common factor = 9 .
Then , the sum of 45 and 27 can be written as :
9 ( 5 + 3 )
Therefore , Mr . Morris wrote = 9 ( 5 + 3 ) .
Solution 6 :Total number of event flyers in a club = 4896
Total number of playerz in a club = 24
Then number of flyers each member of the club will get =
= 4896 ÷ 24
= 204
Therefore , each player will get 204 flyers .
Solution 7 :Part A is not given .
Part B :
= 7950 ÷ 25
= 318
Therefore , 7950 ÷ 25 = 318 .
Which of the following statements describes the value of the expression 35 – 2x, when x = 6?
Answer:
35-2(6)
= 23
Prime number
Step-by-step explanation:
Answer:
23 . It is a prime number.
Step-by-step explanation:
[tex]35 - 2x \\ x = 6 \\ \\ 35 - 2(6) \\ = 35 - 12 \\ [/tex]
Simplify
[tex]23[/tex]
You can use a calculator
Answer:
238, 000
Step-by-step explanation:
hope this helps </3
Line s has a slope of -7/2 line t is perpendicular to a. What is slope of line t
Answer: 2/7
Step-by-step explanation:The slope of perpendicular lines are opposite reciprocals
PLZ HELP 42 POINTS IF U ANSWER I WILL GIVE BRAINEST PLEASE YA'LL What is the product?
Enter your answer as a fraction, in simplified form, in the box.
−14⋅(−611)
Answer:
0.14!
Step-by-step explanation:
Answer:
There is no way I can answer in fraction form, but here is what I calculated: 8554
How many solutions does this equation have
2x + 1 = 2x – 1
Suppose y = 2x – 2.5. Find x if y = 10.
Find the length and width of a rectangle with maximum area that has a perimeter of 9P units.
Answer:
l = 9p/4 , l = 9p/4
Step-by-step explanation:
Given:
Perimeter = 9p
Find:
Length and width
Computation:
Assume;
Length = l
Perimeter = 2(l+b)
9p/2 = l+w
w = 9p/2 - l
Area = lb
Area = l(9p/2 - l)
Using differentiation
l = 9p/4
w = 9p/2 - l
w = 9p/2 - 9p/4
w = 9p/4
does the surface in contact with ground affect the going motion of the car ?why?
Answer:
Yes, it does. The ground is bumpy and it creates friction acting against the car's motion.
(you can include my example too depending on what your teacher is looking for)
Step-by-step explanation:
This is a fun one! Think about a ball rolling on a smooth surface, now on a bumpy sandpapery one. Which one do you think is faster? The smooth surface! This is because of this friction of the sandpaper which slows down the ball. On the other hand, the smooth one has very little friction. The same applies to cars.
Need help on these two questions ♡
Answer:
for question 5 it is the last option
for question 6 it is the 3rd option down
Step-by-step explanation:
2=10 3=18 4=28 6=54 then 8=?
Answer:
72
Step-by-step explanation:
2*5=10
3*6=18
6*8=54
8*9=72
Need help with number 6 I’ll mark you as the brainliest please help.
Answer:
Formula
Step-by-step explanation:
[tex]Equation (y-y1) = m(x-x1)[/tex]
Plug in 8 for x1 and -1 for y1 and 3/4 for m
Solve for y
Use basic math skills
Plz help me it’s geometry
A business knew that 30%, percent of its customers were less than 25 years old. The business wanted to increase this percentage, so they created a marketing campaign that targeted this age group. After the campaign, the business obtained a random sample of 50 customers to test H_o:p=0.3 versus Ha :p > 0.3, where p is the proportion of this business's customers who are less than 25 years old after the marketing campaign. After the campaign, the business obtained a random sample of 50 customers and found that 18 of those sampled were less than 25 years old. What would be the P-value for their test?
Answer:
The answer is "0.9258201 or [tex]\bold{ \frac{0.36 -0.3}{\sqrt{\frac{0.3 \times 0.7 }{50}}}}[/tex]".
Step-by-step explanation:
[tex]\to P= 30 \ \%\\\\ \to x= 18 \\\\ \to n=50\\\\\\\hat p= \frac{x}{n} = \frac{18}{50} = 0.36 \\\\\bold{Formula:}\\\\X= \frac{\hat p -p}{\sqrt{\frac{p \times (1-p)}{n}}}\\\\[/tex]
[tex]= \frac{0.36 -0.3}{\sqrt{\frac{0.3 \times (1-0.3)}{50}}}\\\\= \frac{0.36 -0.3}{\sqrt{\frac{0.3 \times 0.7 }{50}}}\\\\= \frac{0.36 -0.3}{\sqrt{\frac{0.21}{50}}}\\\\= \frac{0.06}{\sqrt{0.0042}}\\\\= \frac{0.06}{0.064807407}\\\\= 0.9258201[/tex]
Answer:
Step-by-step explanation:
7y + 5 = 54 what is y
Answer:
7
Step-by-step explanation:
7x7=49+5=54
Answer:
y = 7
Step-by-step explanation:
Alrighty, here we go!
First step is to subtract 5 from 5 and from 54. Cancel out the 5's.
After doing so, you have 7y = 49.
Now, divide 7 from 7y and from 49. Cancel out the 7's.
Now you have y = 7
There is your answer!
Mark brainliest if possible please :)
f(x) = 3x2 – 4x – 1
g(x) = –2x + 5
Find: (gof)(x)
Answer:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Step-by-step explanation:
The Composite Function
Given f(x) and g(x) real functions, the composite function, named (g\circ f)(x) is defined as:
[tex](g\circ f)(x)=g(f(x))[/tex]
For practical purposes, it's found by substituting f into g.
Given the functions:
[tex]f(x) = 3x^2 - 4x - 1[/tex]
[tex]g(x) = -2x + 5[/tex]
We need to find
[tex](g\circ f)(x)=g(f(x))[/tex]
Replace f into g:
[tex](g\circ f)(x)=-2(3x^2 - 4x - 1) + 5[/tex]
Operating:
[tex](g\circ f)(x)=-6x^2 +8x +2 + 5[/tex]
Reducing:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Thus,
[tex]\boxed{(g\circ f)(x)=-6x^2 +8x +7}[/tex]
HELLLPP!!!! Jake's regular hourly wage is $14.15 after working 40 hours in a week he gets paid overtime which is a pay and a half if Jake worked for 58 hours what will his weekly gross income be
Which equation has the solution x = 9?
Select each correct answer.
+7= 8
4+ 5x = 18
81 – 3 = 6
х
2x – 3 = 15
24 – 2x = 13
3x + 2 = 25
Answer:
2x – 3 = 15
Step-by-step explanation:
2 * 9 = 18 - 3 = 15. correct
+7 = 8, no I don't really now what you mean by this...
81 - 3 = 6x? > (81 - 3 = 78) = (6 * 9 = 54), no, please tell me if I'm interpreting this right.
4 + 5x = 18 > 5 * 9 = 45 + 4 = 49, no
2 * 9 = 18, 24 - 18 = 6, no
3 * 9 = 27 + 2 = 29, no
Find the value of ×
[tex]3x + 2(x - 4) = 14[/tex]
Answer:
x = 22/5
Step-by-step explanation:
3x+2(x-4) = 14
Distribute
3x+2x -8 = 14
5x - 8 = 14
Add 8 to each side
5x-8+8 = 14+8
5x = 22
Divide by 5
5x/5 = 22/5
x = 22/5
Turn -8 1/2 into an improper fraction. Explain your steps
Answer:
-17/2
Step-by-step explanation:
This is the answer because:
1) The formula of turning mixed fractions into improper fractions is:
Denominator x Whole Number + Numerator
2) 2 x -8 = -16, -16 + -1 = -17
Hope this helps!
Jin adds 1 gallon of a water-and-bleach mixture that is 4% bleach to 2 gallons of a
water-and-bleach mixture that is 10% bleach. What percent of the final mixture is bleach?
Answer:
0.08%
(might be wrong)
Step by step explanation:
0.04•1+0.10•2=3•x
0.04+0.2=3x
0.24=3x
x=0.08
Not sure if this is right
Answer: 8
Step-by-step explanation:
Divide the number 484 into two parts in a ratio of 7 : 4. How much bigger is the first number than the second number?
Answer:
I don't known
Step-by-step explanation:
Answer:
132
Step-by-step explanation:
First, obtain the total of the ratio:
7+4 = 11
Then, make equations:
[tex]\frac{7}{11} =\frac{x}{484}[/tex] and [tex]\frac{4}{11} =\frac{x}{484}[/tex]
Next, solve:
11x = 7*484 → 11x = 3388 → x = 308
11x = 4*484 → 11x = 1936 → x = 176
Finally, find the difference:
308 - 176 = 132
(**If it is asking how many times bigger... 308/176 = 1.75 or [tex]\frac{7}{4}[/tex] )
f(x) = 23 – 22
g(x) = 4x + 5
Answer:
23-22=1
5 times 4=20
Step-by-step explanation:
Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Sante Fe program for 2 years.
Student A B C D E F G
SAT Score 421 375 585 693 608 392 418
GPA 2.93 2.87 3.03 3.42 3.66 2.91 2.12
Student H I J K L M
SAT Score 484 725 506 613 706 366
GPA 2.50 3.24 1.97 2.73 3.88 1.58
The least-squares regression equation that shows the best relationship between GPA and the SAT score is:_____.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
SAT SCORE :
421
375
585
693
608
392
418
484
725
506
613
706
366
GPA:
2.93
2.87
3.03
3.42
3.66
2.91
2.12
2.50
3.24
1.97
2.73
3.88
1.58
Using the online linear regression calculator ; the regression model obtained is :
ŷ = 0.00345X + 1.00301
0.00345 = slope or gradient
1.00301 = intercept ; where the regression line crosses the y axis
X = independent variable or predictor variable ; y = dependent variable or predicted variable
lines A and B are parallel lines find the measures of angle 1
Answer:
33Step-by-step explanation:
alternate angles are equal
see attached
The measure of ∠1 is 33° .
What is alternate interior angles?When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
According to the question
As given , lines A and B are parallel lines
therefore ,
∠1 = 33°
∠3 = 57°
they are between parallel line and opposite of transversal line
So, they are alternate interior angles and are equal .
Hence, The measure of ∠1 is 33° .
To know more about alternate interior angles here:
https://brainly.com/question/14693114
#SPJ2
One number is six times as large as a certain smaller number. Let x represent the smaller number.
Write the number that is 20 more than the smaller number.
Answer:
24
Step-by-step explanation:
6x = x + 20
Subtract x from both sides
5x = 20
Divide by 5 on both sides
x = 4
Confirm
4 times 6 equals 24, and 4 + 20 is 24 as well.
What is the slope of y-5= 3x + 4?
Answer:
x=53
y=19
Step-by-step explanation:
3x + y-5
3(5)=15
15+y