given the weekly demand curve of a local wine producer is p= 50-0.1q, and that the total cost function is c= 1500+ 10q, where q bottles are produced each day and sold at a price of $p per unit. a)Express the weekly profit as a function of price.b) at what price must a bottle of wine be sold to realise maximum profit. c) what is the maximum profit that ca be made by the producer
Answer:
a)the weekly profit as a function of price is[tex]P=-10 p^2 + 600 p - 6500[/tex]
b) a bottle of wine be sold at $30 to realise maximum profit
c) the maximum profit that can be made by the producer is $2500
Step-by-step explanation:
The weekly demand curve of a local wine producer is p= 50-0.1q
p = price
q = quantity
Revenue function R =Price \times Quantity
R=(50-0.1q)q
[tex]R=50q-0.1q^2[/tex]
Cost function: c= 1500+ 10q
Profit function=R(x)-C(x)
Profit function= [tex]50q-0.1q^2-1500-10q[/tex]
Profit function= [tex]40q-0.1q^2-1500[/tex] ----1
We have q = 500 - 10 p using p = 50 − 0.1q
[tex]P=-0.1 (500 - 10 p)^2 + 40 (500 - 10 p)- 1500\\P= -10 p^2 + 600 p - 6500[/tex]
General quadratic equation:[tex]ax^2+bx+c=0[/tex]
On comparing
a = -0.1 , b = 40 , c = -1500
Maximum Profit is at q = [tex]\frac{-b}{2a}=\frac{-40}{2(-0.1)}=200[/tex]
To find price must a bottle of wine be sold to realise maximum profit
p= 50-0.1q
p= 50-0.1(200)=30
Substitute the value of q in profit function(1) get the maximum profit
So, Profit function= [tex]40\left(200\right)-0.1\left(200\right)^{2}-1500=2500[/tex]
Hence
a)the weekly profit as a function of price is[tex]P=-10 p^2 + 600 p - 6500[/tex]
b) a bottle of wine be sold at $30 to realise maximum profit
c) the maximum profit that can be made by the producer is $2500
- |4x+10|-7=-14 solve for x
Answer:I forgot how to solve that
Step-by-step explanation:
evaluate x2+x-12÷y2 for x = 5 and y =2
Answer:
3
Step-by-step explanation:
does anybody know the awnser to w=7a+4b
Answer:
w=7a+4bw-4b = 7a
Step-by-step explanation:
Calcule o valor de x, sabendo que as retas “e” “f” e “a” são paralelas
a)36
b)37
c)37,5
d)38
Answer:
c
Step-by-step explanation:
[tex]\frac{x}{25}=\frac{60}{40}\\\\By\:Thales's\:Theorem\\\\x=\frac{60*25}{40}\\\\x=\frac{60*5}{8}\\\\x=\frac{15*5}{2}\\\\x=\frac{75}{2}\\\\x=37.5[/tex]
need help with this
Answer:
Slope-int form: y = 3x+5
Standard form: y - 3x = 5.
Step-by-step explanation:
(reminder: slope-intercept form is expressed as y=mx+b, and standard form is expressed as ax+bx=c.)
Since the slope is 3, the coefficient of x is also 3, which makes the equation y=3x.
But the y coordinate of the equation at x = -2 is -6, so we need to add 5 to the end of the equation, leaving you with:
y=3x+5.
To convert it to standard form, subtract 3x from both sides:
y - 3x = 5.
I hope this helped you.
your hair is 5/16
inch long. Write this length as a decimal.
Answer:
0.3125
Step-by-step explanation:
in decimal form. Use our fraction to decimal calculator to convert any fraction to a decimal and to know if it is a terminating or a recurring (repeating) decimal.
Answer:
0.3125
Step-by-step explanation:
Find the measure of the exterior angle.
64
76
Using the exterior angles theorem, the measure of the exterior angle(k) is 140 degrees.
How to find the exterior angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
The two remote interior angles are 76 degrees and 64 degrees.
Therefore,
76 + 64 = k
k = 140 degrees.
learn more on exterior angles theorem here: https://brainly.com/question/13904180
#SPJ1
In the graph of an inequality, the area above a solid line through the points (−5, 2) and (3, 2) is shaded.
Which inequality does this graph represent?
A. y ≥ 2
B. y ≤ 2
C. y 2
Answer:
A. y ≥ 2
Step-by-step explanation:
First the line is solid, a complete line not dotted so the inequality sign to use is : ≥ or ≤
The points have their y-coordinate vale as 2, (−5, 2) and (3, 2), this means the line crosses the y-axis at y=2 but because the shaded part is above this line, then the correct inequality will be :
y ≥ 2
See attached graph below.
x = -7y; 2x - 8y = 22
Answer:
(7; -1)
Step-by-step explanation:
Hi there!
Here is a solution:
If x=-7y then -14y-8y=22 => y=-1 and x=7
Hope this helps)
Have a nice day!
An amusement park charges $20 to enter the
park and an additional fee for each time a guest
rides a roller coaster. Emily rode 5 times on a
roller coaster. Her total payment was $40.
Shaheem rode 7 times on a roller coaster. What
was his total payment?
Answer:
Shaheem paid $76 as his total.
Step-by-step explanation:
He paid $20 to get in, Emily paid $40 for 5 rides, and if you divide that to get the payment for one ride which is $8. So you multiply 8 by 7 because 7 is how many rides he rode which equals to 56, plus 20(his enter fee) would be $76.
if PQ = 5 and QR = 17 , find PR
PR would be 17.72 as the hypotenuse, according to the measurements, is 17.72
1 1 1
-x -xxxx -x 1 1
=
11 1 1 1
x 1 1 1 1 1
X
1
1
The model represents an equation. What value of x makes the equation true?
A)
3
4
B)
9
2
3
4
D)
9
2.
Answer:
its d or b
Step-by-step explanation:
Answer:i think it is d
Step-by-step explanation:
In order to become a member of the library-all-star-members club, there is a $40 sign-up fee and a $2monthly fee. Write an equation in slope- intercept form that models this situation
Answer:
y = 2x + 40
Step-by-step explanation:
Y is the total cost.
2 is dollars per month.
X is the number of months.
40 is the sign up fee.
Answer:
2x+40
Step-by-step explanation:
what is 4 divided by 6
Verify the following: 3
−21 × −4 + −6 = −21 × −4 + (−21) × (−6)
Answer:
the answer is -14 how about
study math next time
Answer:
Incorrect
Step-by-step explanation:
Use PEMDAS
Solve one side of the equation first
-21 × -4 + - 6
negative × negative = positive
84 + - 6
positive + negative = negative
84 - 6
78
Now solve the other side of the equation
-21 × -4 + (-21) × (-6)
negative × negative = positive
-21 × -4 + (126)
negative × negative = positive
84 + 126
210
Does 78 = 210?
No, so we can assume this equation is incorrect
9=4(s-3)
Help me what’s the correct answer?
Answer:
s=5 1/4
Step-by-step explanation:
Have a wonderful day
If angle knm=(8x-5) and angle mnj=(4x-19) find the measure of angle knm?
45 ahuevo que ssik 45
which angle is this??
Answer:
acute
Step-by-step explanation:
the angles are all less than 90°
they are not equal so not equialteral
has to be acute
An item is priced at $14.07. If the sales tax is 5%, what does the item cost including sales tax?
Answer:
14.77
Sale Tax: 5.00% or $0.70
Answer:
14.12
Step-by-step explanation:
0.05 is also known as 5%
14.07+0.05=14.12
Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared.
Answer:
Hope this helps...
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
9x - 5 = 7x + 3
2x = 8
x = 4
Jill babysat for 7 1/2 hours and earned $63.75. How much money does she earn per hour?
Answer:
$8.50 per hour
Step-by-step explanation:
63.75 / 7.5 = 8.5
A local pizza shop has a membership program for frequent buyers. The membership costs $10 per month and members get a discounted price of $1.75 per slice of pizza. Autumn purchased a membership to this pizza shop.What would be the monthly cost for xx slices of pizza?
Answer:
Monthly cost = $10 + $1.75x
Step-by-step explanation:
Given the following :
Membership cost = $10 per month
Discounted price for members = $1.75 per slice of pizza
If Autum purchased the membership, the monthly cost for x slices of pizza
Monthly cost of x slices will be :
Membership cost + (discounted price * number of slices)
Monthly cost = $10 + ($1.75 * x)
Monthly cost = $10 + $1.75x
Help!! Please! Its algebra!!
Answer:
y - 7 = -4 ( x -2 )
Step-by-step explanation:
just use the given informations:
The base formula:
y - y(1) = m ( x -x(1) )
remember that "m" typically refers to the slope of a line
There is a given set of points on the line: (2, 7)
hence just plug in the numbers:
x(1) = 2
y(1) = 7
m = -4
and you get
y - 7 = -4 ( x -2 )
Y=-4(x-2)
hope it helps
What is 5280 divided by 60
Answer:
ya the answer is 88
Step-by-step explanation:
what is 4x +9 in a verbal expression?
Answer:
four times a number plus nine
Step-by-step explanation:
Solve sx+tx=r for x?
Answer:
x= r/s+t
Step-by-step explanation:
Solve the following inequality:
4(x - 6) < 3x + 13
Answer:
x < 37
Step-by-step explanation:
4(x - 6) < 3x + 13
Distribute
4x -24< 3x+13
Subtract 3x from each side
4x-3x -24 < 3x+13-3x
x-24 < 13
Add 24 to each side
x-24+24 <13+24
x < 37
Step-by-step explanation:
4(x-6) <3x+13
4x-24<3x+13
CLT
4x+3x<13-24
7x<-11
x= -11/7
4. Landon is cooking soup. He has 15 pinan of vegetable broth, 19 pints of milk, and 14 pints of tomato juice. How many gallons does Landon have, if 1 gallon = 8 pints? 6 gallons.
Answer:
6 gallons
Step-by-step explanation:
1) add 15 and 19 to get 34
2) then add 34 and 14 to get 48
3) then divide 48 by 8 to get 6