The weekly revenue for a product is given by R(x) = 324x - 0.0495x?, and the weekly cost is C(x) = 8000 + 162x - 0.099x2 + 0.00003x”, where x is the number of units
produced and sold
(a) How many units will give the maximum profit?
(b) What is the maximum possible profit?
(a) The number of units that will give the maximum profit is
(Round to the nearest whole number as needed.)
Answers
Answer:
(a) The number of units that will give the maximum profit is 2,000 units.
(b) The maximum possible profit is $274,000.
Step-by-step explanation:
(a) How many units will give the maximum profit?
From the attached photo in the question, we are given;
R(x) = 324x - 0.0495x^2 ………………....................................……….. (1)
C(x) = 8000 + 162x - 0.099x^2 + 0.00003x^3 …………………….. (2)
In economics, profit function, P(x), is obtained as follows:
P(x) = R(x) - C(x) ………………………. (3)
Substituting the equations (1) and (2) for R(x) and C(x) respectively into equation (3) and then simplify, we have:
P = 324x - 0.0495x^2 - (8000 + 162x - 0.099x^2 + 0.00003x^3)
P = 324x - 0.0495x^2 - 8000 - 162x + 0.099x^2 - 0.00003x^3
P = -8000 + 162x + 0.0495x^2 - 0.00003x^3 ………………….. (4)
Taking a derivative of equation (4) with respect to x and equating to 0, we have:
162 + 0.099x - 0.00009x^2 = 0 .................... (5)
Using the almighty formula as follows:
x = (-b +/- (b^2 - 4ac)^0.5) / 2a ………………. (6)
Where, from equation (5);
a = - 0.00009
b = 0.099
c = 162
Substituting the values into equation (6), we have:
x = (-0.099 +/- (0.099^2 - (4 * (- 0.00009) * 162))^0.5) / (2 * - 0.00009)
x = (-0.099 +/- 0.261) / -0.00018
x = (-0.099 + 0.261) / -0.00018, or x = (-0.099 - 0.261) / -0.00018
x = -900, or x = 2000
Since negative number does not have economic value in economics, the number of units that will give the maximum profit is therefore 2,000 units.
(b) What is the maximum possible profit?
From part a, x = 2000
Substituting x = 2000 into equation (4) and then solve, we have:
P(x) = -8000 + (162 * 2000) + (0.0495 * 2000^2) - (0.00003 * 2000^3)
P(x) = 274,000
Therefore, the maximum possible profit is $274,000.
Related Questions
Examine the worked problem and solve the equation.
Four-thirds (x) minus one-third = 9. Four-thirds (x) minus one-third + one-third = 9 + one-third. Four-thirds (x) = StartFraction 28 over 3 EndFraction
The solution is x =
.
Answers
Answer:
The answer is 7
Step-by-step explanation:
I don't know how to explain it really but just divide 4/3 by 28/3 and you should get the answer of x
Answer:
7
Step-by-step explanation:
For a taxi driver, which measures must be accurate? Check all that apply.
A. Price per mile
B. Distance traveled by customer
C. Price if gasoline per gallon
D. Number of customers per day
Answers
Answer:
Them all as he has to know how far he travels the customer rate to see is there is an increase of decrease price of gasoline to see if it's affecting g his outcome and price per miles for obvious reasons haha
Answer:
the answer B. Distance traveled by customer
Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 -3 2 -9 3 -15 4 -21
Answers
Answer:
The numbers:
1, -3, 2, -9, 3, -15, 4, -21,
are not linear.
Step-by-step explanation:
If it was linear:
4, 3, 2, 1, -3, -9, -15, -21
Morris Katz bought four new tires at Goodyear for $95.85 per tire. Goodyear also charged Morris $2.68 per tire for mounting, $2.58 per tire for valve stems, and $4.13 per tire for balancing. Assume no tax.
What was Morris’s total cost for the four tires?
Round your answer to 2 decimal places.
Answers
Answer:
$420.96
Step-by-step explanation:
95.85+2.68+2.58+4.13=$105.24
105.24*4=$420.96
solve the following two equation X+Y=5
X-2Y=2
Answers
Step-by-step explanation:
x=4 and y= 1 because of 4+1=5 and add 2y to both sides
x-2y+2y=2+ 2y
x=2y+2
4-2=2
[tex]\left \{ {{x+y=5} \atop {x-2y=2}} \right.[/tex]
Here we have 2 equations in one system.
System of Equations/Simultaneous Equations are for finding the intercepts of both graphs.
We can solve these Simultaneous Equations in many ways. However, I'll be solving by substitution.
To solve by using substitution, we need to move either x or y to the another side. I'll move x term to another side for the first equation. (We'll substitute the first equation in the second.)
[tex]\left \{ {{y=-x+5} \atop {x-2y=2}} \right.[/tex]
Now we substitute y = -x+5 in x-2y = 2
[tex]x-2(-x+5)=2\\[/tex]
Then distribute -2 in (-x+5) | Note that multiplying the negative will get positive. |
[tex]x-2(-x+5)=2\\x+2x-10=2\\3x=2+10\\3x=12[/tex]
We should get this. When we get this, we move 3 to divide 12 (Opposite when moving to another side so from plus to minus and from multiply to divide.)
[tex]x=4[/tex]
But we are not done yet. We have to find the y-value. After all they are two variables equations.
If we want to find the y-value then we have to substitute x = 4 in any given equations. I'd suggest to substitute in the equation that doesn't have a coefficient with high value.
So I'll be substituting in x + y = 5 instead.
Substitute x = 4 in x + y = 5
[tex]4+y=5\\y=5-4\\y=1[/tex]
Thus, we get both x and y value. Answer in either coordinate point or writing form.
Therefore, the answer is
x = 4 when y = 1 or (4,1)
Both works. Hope this helps.
The GCF of 18 and 27 is _______. Numerical Answers Expected! Answer for Blank 1:
Answers
Answer:
9
Step-by-step explanation:
GCF = Greatest Common Factor
The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 27 are 1, 3, 9, 27. The common factors of 18 and 27 are 1, 3 and 9. The greatest common factor of 18 and 27 is 9.Answer:
9
Step-by-step explanation:
Which expressions represent the sum of exactly two terms?
Choose 2 answers:
(Choice A)
xy
(Choice B)
m^4+6n
(Choice C)
3+7s+t
(Choice D)
a+c
Answers
Answer:
Step-by-step explanation:
The answer is a+c and 3+7s+t
Bacuase both term have single power
Graph the logarithmic function below by moving the
key point.
y = log₂ (x)
You can only graph integer points
Answers
To graph the logarithmic function y = log₂(x), we can use the key point (1,0) and the fact that the logarithmic function is the inverse of the exponential function y = 2ˣ.
Starting at the key point (1,0), we can move to the right by increasing x by a factor of 2, since log₂(2) = 1. This takes us to the point (2,1). Similarly, we can move to the right by a factor of 2 again to get to the point (4,2), and then to (8,3), (16,4), and so on.
If we instead move to the left from the key point (1,0) by a factor of 2, we get to the point (1/2, -1), since log₂(1/2) = -1. We can continue moving to the left by dividing x by 2 to get to (1/4, -2), (1/8, -3), and so on.
The given graph of y = log₂(x) using only integer points.
The graph is symmetric about the line x=1, since log₂(x) = log₂(1/x) = -log₂(x).
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If Jack's salary went from $15 per hour to $17 per hour this year, find the percent increase
Answers
Answer: 13%
Step-by-step explanation:
17$-15$ = 2$
15$ x 0.13 = 1.95$
I NEED HELP PLS ON THIS QUESTION ON MY STUDY GUIDE
Answers
Answer:
4(n + 3) = 60
Step-by-step explanation:
In the question it says '3 more than the usual' and that is a big hint that it is 4(n + 3) = 60
Simplify the expression: 6+p–8+7
Answers
Answer:
p+5
Step-by-step explanation:
I feel as if I might be oversimplifying my answer, so I may be wrong. But, I simply took the time to add like terms! The variable- p- will stand alone because it does not have a given value. The 6, 7, and -8 can be added together, though! Hence my +5. I hope this helped! :)
someone please help me with this!
Answers
Answer:
remove the bracket on the other side by multiplying 180 by (2-n)
subtract 360 from 1260 to remain with -180n on the other side
divide both sides by -180n
then n become -5
A total of 160 children play in the city soccer league and 64 of the players are girls what percent of the players are girls
Answers
Answer:
40 percent of the children that play soccer are girls in the league
Step-by-step explanation:
just divide 64/160 and get 40
Answer:
40%
Step-by-step explanation:
64/160 = 0.4
0.4 = 40%
PLZ HELP ME
1: Suraj says the two expressions below are equivalent. Is he correct? 2(3d - 2) and 6d - 2
A: No, when you distribute 2(3d - 2) you get 3d - 4 .Suraj did not distribute correctly.
B: Yes, when you factor 6d - 2 you get 2(3d - 2)
C: No, when you distribute 2(3d - 2) you get 6d - 4. Suraj did not multiply 2 by -2 correctly
D: Yes, when you distribute 2(3d - 2) you get 6d - 2.
2: Using the expressions (3x - 5y) and (4x + 2y),find the sum of the two given expressions.
A: 7x + 7y
B: 7x + 3y
C: x - 7y
D: 7x - 3y
3: Using the expressions (3x - 5y) and (4x + 2y), find the difference of the two given expressions.
A: -x - 7y
B: x - 3y
C: x - 7y
D: x + 3y
4: Factor: 30a + 35b.
A: 5(6a + 7b)
B: 5b(6a + 7)
C: this expression is already factored
D: 5a(6 + 7b)
Answers
4.a
i don’t know the answers to 2 and 3 but i hope this helps
PLEASE ANSWER THIS
Review the problem below. Determine when the Associative, Commutative , and Additive Inverse properties are used.
Original problem (5.2 - 4) -4 + 6.2
Step One (5.2 - 4) +(-4) + 6.2
Step Two 1.2 + (-4) + 6.2
Step Three 1.2 + 6.2 + (-4)
Step Four (1.2 + 6.2) + (-4)
Step Five 7.4 + (-4) = 3.4
Answers
Answer:
2.5
Step-by-step explanation:
PLEASE HELP MEEEEEEEEEEEEEE ILL GIVE U 50 coins for the right answer
Simplify the expression. Explain each step (0+c)+12
Answers
Answer:
x+12
Step-by-step explanation:
(0+c)+12
0+c+12
c+12+0
c+12
Hope this helps plz hit the crown :D
The problem to solve is:
(0+c)+12
0+c evaluates to +c
0 + 12 = 12
The answer is 12+c
(0+c)+12 evaluates to 12+c
The final answer is
12+c
IF THE RATIO IN A VALENTINE'S
DAY CANDY BOX OF MILK TO DARK
CHOCOLATES IS 23. HOW MANY
DARK CHOCOLATES ARE THERE IF
THERE ARE 8 MILK CHOCOLATES?
Answers
Answer:
12 dark chocolates
Step-by-step explanation:
Let there are 2x milk chocolates and 3x dark chocolates.
Total no of milk chocolates = 8
ATQ,
2x = 8
x = 4
Dark chocolates = 3x
= 3(4)
= 12
Hence, there are 12 dark chocolates.
Plot and label 3 different points with x-coordinate 3.
Answers
These all hav the x cord of 3
Plz giv brainlyest Bro I need it
Find the sum of -8x^{2}+9x−8x 2 +9x and -6x^{2}+10x−6x 2 +10x.
Answers
Answer:
-14x² +19x
Step-by-step explanation:
You want the sum of the expressions (-8x² +9x) and (-6x² +10x).
SimplificationThe sum is found by adding like terms: terms with the variable to the same power.
(-8x² +9x) + (-6x² +10x)
= (-8 -6)x² +(9 +10)x
= -14x² +19x
-3 < x -10 Solve for X and simplify please
Answers
Hey there!
“-3 < x - 10”
SOME people treat the “<” “>” as an equal sign to make these types of problems easier to solve!
-3 = x - 10
Flip the equation around
x - 10 = -3
ADD both of your sides by 10
Like: x - 10 + 10 = -3 + 10
CANCEL out: -10 + 10 because it gives us 0
Keep: -3 + 10 because it gives us the value of x
-3 + 10 = x
Solve that above and you have your answer: x = 7 ☑️
Overall answer: x < 7
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
I was just wondering what the explanation and answer to this problem would be?
Answers
Answer: Acute ask goigle
Find each angle measure in the triangle.
3x°
2xº
4xº
Answers
The total measure of angles in a triangle is 180°.
3x° + 2x° + 4x° = 180°
9x° = 180°
x° = 180° ÷ 9
x° = 20
Our 3 angles are:
3(20) = 60°
2(20) = 40°
4(20) = 80°
Done.
Answer:
Step-by-step explanation:
3x+2x+4x=180
9x=180
x=180/9=20
3x=3×20=60°
2x=2×20=40°
4x=4×20=80°
Scientists are preparing two satellites to be launched. The equation y=8200xy=8200x represents the number of miles, yy, that the satellite, Space Explorer B, flies in xx hours. The satellite, Space Explorer A, flies 28800 miles in 24 hours.
How many fewer miles does Space Explorer A travel in one hour than Space Explorer B?
Answers
Answer:
Space Explorer B travels 6800 miles more than Space Explorer A in one hour.
Step-by-step explanation:
Space Explorer A travels 7000 miles less than Space Explorer B in one hour.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Space Explorer A flies 28800 miles in 24 hours.
24 hours = 28800 miles
1 hour = 28800/24 miles
1 hour = 1200 miles
Hence, Space Explorer A travels 1200 miles in 1 hour.
Now, the equation representing the distance, y, traveled by Space Exploral B in x hours is:
y = 8200x
Substitute x = 1:
y = 8200
Therefore, Space Exploral B travels 8200 miles in 1 hour.
The difference between the distance traveled by Space Exploral B and Space Exploral A is:
8200 - 1200
= 7000
Hence, Space Explorer A travels 7000 miles less than Space Explorer B in one hour.
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please help me asap
Answers
With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount? Hint: First subtract to find the amount of discount$, then divide it by the original price.
Answers
Answer:
14[tex]\frac{2}{7}[/tex]%
Step-by-step explanation:
We can just follow the hint.
Amount of discount = $84 - $72
= $12
Percentage of discount = [tex]\frac{12}{84}[/tex] × 100%
= 14[tex]\frac{2}{7}[/tex]%
Answer:
14.3% discount.
Step-by-step explanation:
Heya! So by the hint that they gave us, I subtracted 72 from 84, and then divided the 12 by 84. The true answer is 0.143 (rounded to the hundredth), getting you close to the initial 12. I hope this helped at least a little bit!
Adult and student tickets to the high school basketball game are sold each week. for every two adult tickets seven students tickets are sold. how many total tickets were sold if 92 adult tickets were sold?
Answers
Answer:
414
Step-by-step explanation:
the ratio of adult tickets to student tickets = 2 to 7 num of student tickets / 92 = 7 / 2 ... x = 414 total tickets sold.
Find the domain and range of the following functions:
1. f(x) = 4x-3
2. G(x) = | 1-2x |
3. f(x) = x²-2x+1 / x-1
Answers
The domain and range of the functions, Domain includes all possible inputs and range includes all possible outputs , are-
1. f(x) = 4x-3
Domain - all real numbers or
Range - all real numbers
2. G(x) = | 1-2x |
Domain- all real numbers
Range - All real numbers≥ 0
3. f(x) = x²-2x+1 / x-1
this can be simplified as ( x-1)²/(x-1) = x-1
Domain - all real numbers
Range- all real numbers
4. f(x) = {x-1 if x<3,
2x+1 if x ≥3 }
Domain - all real numbers
Range - All real numbers
5. y = [tex]\sqrt{4-x}[/tex]
Domain - All real numbers <4
Range - all real numbers ≥0
Mathematical functions are analogous to vending (soda) machine operations. When you put in a certain amount of money, you can choose from a variety of sodas. Similarly, when we use functions, we enter different numbers and get new numbers as a result. The primary characteristics of functions are domain and range. A soda can be purchased with quarters or one-dollar bills. If you put in pennies, the machine will not give you any soda flavor. As a result, the domain represents the inputs available here, which are quarters and one-dollar bills. A cheeseburger will not be served from a soda machine, no matter how much you pay. Thus, the range represents the possible outputs we can have here, i.e., the
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What can 7/8 be rewritten as?
Answers
Answer:
0.875
Step-by-step explanation:
Answer:
Step-by-step explanation:
u would divide 7 by eight and get 0.875
Fred buys flags from a manufacturer. For f dollars each and then sells the flags in his store for a 26% markup . write an expression for the retail price of a flag
Answers
Answer:
f - 0.26f
Step-by-step explanation:
GIVING BRAINIEST IF CORRECT!!!!
Express the product in simplest form.
Answers
Answer:
i bite my tongue its a baddd habit
28 + 10√3
Step-by-step explanation:
first, multiply the two together. √3 * √3 = 3. √3 * 5 = 5√3. 5 * √3 = 5√3. 5 * 5 = 25.
We have 3 + 5√3 + 5√3 + 25. Combine like terms and you should get 28 + 10√3.