A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the total cost and total revenue in thousands of dollars are
C(x,y)=2x 2 −2xy+y 2 −7x−9y+11
R(x,y)=7x+9y.
Find the number of each type of product that should be manufactured to maximize profit. (Assume that profit will be maximized at its critical point.)
x=
y=
What is the maximum profit? thousand dollars
Answers
To maximize profit, we need to find the critical point(s) of the profit function, P(x, y). Profit is defined as the difference between total revenue and total cost. Thus, the maximum profit is 49 thousand dollars.
The profit function is:
P(x, y) = R(x, y) - C(x, y)
Now substitute the given functions for R(x, y) and C(x, y):
P(x, y) = (7x + 9y) - (2x^2 - 2xy + y^2 - 7x - 9y + 11)
Simplify the profit function:
P(x, y) = -2x^2 + 2xy - y^2 + 14x
Next, find the partial derivatives of the profit function with respect to x and y:
∂P/∂x = -4x + 2y + 14
∂P/∂y = 2x - 2y
To find the critical point(s), set both partial derivatives equal to zero and solve the system of equations:
-4x + 2y + 14 = 0
2x - 2y = 0
Solve for y in the second equation:
y = x
Substitute y = x in the first equation:
-4x + 2x + 14 = 0
-2x + 14 = 0
Solve for x:
x = 7
Now, substitute x back into y = x to find the value of y:
y = 7
So, the number of each type of product that should be manufactured to maximize profit is x = 7 and y = 7, or 7,000 units of product A and 7,000 units of product B.
To find the maximum profit, substitute the values of x and y into the profit function:
P(7, 7) = -2(7^2) + 2(7)(7) - (7^2) + 14(7)
P(7, 7) = -98 + 98 - 49 + 98
P(7, 7) = 49
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Related Questions
An optical inspection system is used to distinguish among different part types. The probability of correct classification of any part is 0. 98. Suppose that three parts are inspected and that the classifications are independent. Let the random variable x denote the number of parts that are correctly classified. Determine the probability mass function and cumulative mass function of x.
Answers
The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.
The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.
Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.
The PMF of x is given by the binomial probability formula:
P(x) = (n C x) * p^x * (1 - p)^(n - x)
where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).
In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).
Let's calculate the PMF for x:
P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004
P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588
P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432
P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192
The PMF for x is:
P(x = 0) = 0.0004
P(x = 1) = 0.0588
P(x = 2) = 0.3432
P(x = 3) = 0.941192
To calculate the CMF, we sum up the probabilities up to x:
F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)
Using the calculated probabilities, the CMF for x is:
F(x = 0) = 0.0004
F(x = 1) = 0.0592
F(x = 2) = 0.4024
F(x = 3) = 1.0
Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.
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To evaluate 8^2/3 find
Answers
To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the powers they possess, many rules of exponents are given.
Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
The given value can be written as:
\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)
Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
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Flora drew the following graph to answer the question. What was her mistake when she drew her graph? (NO LINKS)
Answers
Answer:
Her elevation went down too quickly, if she is going down 300 ft per hour at a constant rate, at 1 hour, she should be at 2700 feet. It should take her about 10 hours to get down the mountain.
Determine the volume of this shape in terms of pie please show work
Answers
Answer:
\(\pi432 {cm}^{3} \)
Step-by-step explanation:
The formula to calculate the volume of a cone is
\(v = \frac{(\pi {r}^{2})h }{3} \)
Since they asked that we determine the volume in terms of pi, we are not going to equate pi to its numerical value.
\(r = 9 \: \: \: \: \: \: \: \: h = 16\)
I am not sure if the radius is 9 cm because the image is kinda blurry. If it is not 9 cm you can input the actual radius into the formula to find the volume.
\(v = \frac{(\pi {r}^{2})h }{3} \\ v = \frac{(\pi {9}^{2} )16}{3} \\ v = \frac{(\pi81)16}{3} \)
\(v = \frac{\pi1296}{3} \\ v = \pi432\)
The graph of y=3x is shown. What is the value of x when y=27?
A. 2
B. 3
C. 9
D. 24
It said c was wrong
Answers
Answer:
x = 3
Step-by-step explanation:
Is x an exponent?
\( y = 3^x \)
\( 27 = 3^x \)
\( 3^3 = 3^x \)
\( x = 3 \)
In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1200?
Answers
1200 parts/ 400 parts = 3
12 parts x 3 = 36 parts
In 1200 parts, 36 would be bad.
What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-4y=24
Answers
Answer:
y = -4x - 1
Step-by-step explanation:
x - 4y = 24
-4y = -x + 24
y = \(\frac{1}{4}\)x - 6
m⊥ = -4
y = -4x + b
7 = -4 ( -2 ) + b
7 = 8 + b
b = -1
y = -4x - 1
Age
Rick is ten years older than his brother Jeff.
In four years, Rick will be twice as old as
Jeff. How old is Jeff now.
Answers
Answer: I think Rick is 16 and jeff is 6
Jayden used 20 color ties to make a design above his stove 15 out of 20 of his tires were green what is an equivalent fraction for the green tie
Answers
Answer:
3/4
Step-by-step explanation:
15.20 simplified = 3/4
Which of the following statements must be true about this diagram? Check all that apply.
Answers
The following are the true statements are
m<4 is greater than m<2
m<4 is greater than m<1
m<1 + m<2= m<4
What is exterior angle property?If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
As, by property
m<1 + m<2= m<4
and, the measure of each individual angle is less than angle 4.
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The length of an arc of a circle is 7.5 cm. The corresponding sector area is 37.5 cm². The radius is 5cm.
Find the angle subtended at the centre of the circle by the arc.
Answers
Answer: Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm. From the given arc length of 7.5cm, the subtended angle at the circle center theta radian can be Theta /2π =7.5/2πr or
Theta radian =7.5/r. For the radian, 7.5/r subtended angle sector area can be 7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2. We already have given sector area as 37.5, then 7.5r/2=37.5, or r will be 37.5*2/7.5 which gives us 10.
Step-by-step explanation:
Let us assume that the radius of the circle is r where the corresponding sector area and arc length are 37.5sq. cm and 7.5cm
By the arc length of 7.5cm, the subtended angle at the circle center theta radian will be
Theta /2π =7.5/2πr or
Theta radian =7.5/r
For the 7.5/r radian subtended angle sector area is
7.5/r/2π^2 or 7.5/2πr*πr^2 or 7.5r/2
We have given the sector area 37.5, so now 7.7r/2=37.5, or
r=37.5*2/7.5=10cm
suppose that sin ( θ ) = 0.514 sin(θ)=0.514. y y is how many times as large as r r?
Answers
The y is approximately 1.224 times as large as r.
we first need to recall the definitions of sine and the Pythagorean theorem. Sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle, or sin(θ) = y/r. The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two sides that form the right angle) is equal to the square of the hypotenuse, or a^2 + b^2 = c^2.
Using the given information that sin(θ) = 0.514, we can set up the equation y/r = 0.514. Solving for y, we get y = 0.514r.
To find how many times larger y is than r, we divide y by r:
y/r = 0.514r/r = 0.514.
Therefore, y is approximately 1.224 times as large as r.
the ratio of y to r in a right triangle with sin(θ) = 0.514 is approximately 1.224.
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What is the value of (-5)^4?
Answers
Answer: 625
Step-by-step explanation:
8. Jase earns $5.00 per lawn mowed and $5.00 per car washed. Let m be the number of lawns mowed and let c be the number of cars washed. Select all the expressions that could represent the total earned, in dollars, by Jase. A 5(m + c) (B) 5m + c C 5+mc D 5c + m E 5m+5c
Answers
The expressions that can be used to represent the total earned amount is 5(m + c) and 5m + 5c (option A and D).
What are the expressions that represent the total amount earned?In mathematics, an expression is a statement that is made up variables and numbers that are linked together by a mathematical operation.
The total amount earned by Jase is the sum of the total amount earned from mowing the lawn and from washing cars.
Total amount earned = total amount earned from washing cars + total amount earned from mowing lawns
Total amount earned = (cost per lawn mowed x total lawns mowed) + (cost per car washed x number of cars washed)
Total amount earned = ($5 x c) + ($5 x m)
Total amount earned = $5c + 5m
Total amount earned = $5( c + m)
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how much markup is $75 to $180
Answers
Answer:
105
Step-by-step explanation:
75+105 =180
A line passes through the points (–6, 4) and (–2, 2). which is the equation of the line? y = negative one-half x 1 y = one-half x 7 y = –2x – 8 y = 2x 16
Answers
The equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)
What is the equation of the line?
To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
The slope of the line can be found by using the two points:
m = (y2 - y1) / (x2 - x1)
So,
m = (2 - 4) / (-2 - (-6)) = -2/4 = -1/2
We know that the line passes through the point (-6,4) so we can substitute the values into the equation:
y - 4 = -1/2(x + 6)
Hence, the equation of the line that passes through the points (-6,4) and (-2,2) is y - 4 = -1/2(x + 6)
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36. Factorize x-12x + 20
Answers
x intercept of y = x-7
Answers
The x-intercept of the linear equation is (7, 0).
How to find the x-intercept of the linear function?Here we have the following linear equation:
y = x - 7
We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.
0 = x - 7
Solving that, we get:
7 = x
Then we conclude that the x-intercept of the linear equation is (7, 0).
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Simplify 9 to the 2nd power\ 9 to the 7th power
Answers
Answer:
9^2/9^7 = 9^-5
Step-by-step explanation:
An experimenter studies vision in low light by
having participants sit in a darkened room for
either 5, 15, or 25 minutes and then testing their
ability to correctly identify 20 objects. (a) What is
the independent variable here? (b) What are the
conditions? (c) What is the dependent variable?
(d) You would use the scores from which variable
to create a frequency distribution?
Answers
Answer:
Independent variable- time spent in the dark room
Dependent variable - number of objects correctly identified
Conditions of the experiment- low light environment and lighted environments
Scores from the independent variable are used to construct the frequency distribution
Step-by-step explanation:
The independent variable is the factor that is being manipulated in an experiment and this time it is the time spent in a darkened room.
The dependent variable is the response variable, in this case, the number of objects correctly identified.
The experimental conditions involved bringing people from a lighted area into a darkened room.
The variance of a distribution is 195. What is the standard deviation, rounded to the nearest thousandth? fill in the blank 1
Answers
Answer:√29.5= 5.43139
Step-by-step explanation:
triangle sum theorem
WILL MARK BRAINLIEST
Answers
Step-by-step explanation:
13) 4x-22+x+11+10x-4 =180
15x=195
x=13
<P=(10(13)-4)=126
<Q=(4(13)-22)=30
<R=13+11=24
Which point represents the origin? number line from minus 5 to 5 with point M at minus 4, J at minus1, W at 0, and K at 2. Question 1 options: Point W Point J Point M Point K
Answers
The point that represent the origin in the number line is Point W
What is a number line?A number line is a horizontal representation of numbers in parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right
number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p
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Please help me on this, I can't understand this at all!
Answers
Answer:
a) -0.5 • 1.7 - 0.5 • 1.7
Step-by-step explanation:
I knew this answer. It is in distributive property.
I’d like to conduct a study to see the effect of certain diets on Diabetic individuals. We randomly select a sample of 50 people who are known diabetic. I then divide them in two groups randomly. To one group we supply them with the Fried foods and Fast foods and the other group we feed them low Fat food and Proteins and find the initial change in their average blood sugar level. We can compare this change in Blood sugar level to find out if there is a significant difference between the two groups Using the independent sample T test.
What is the null and alternative hypothesis of this study? And would you choose to use a 1-tailed test or a 2-tailed test? What significance (alpha) value would you choose and why?
How would you go about testing this hypothesis statistically? What are the steps you'd go through? (I'm not really asking you to do the calculation, just walk us through the steps).
Answers
The null hypothesis for the given study would be that there is no significant difference between the two groups when it comes to the average blood sugar level.
In contrast, the alternative hypothesis would be that there is a significant difference between the two groups regarding the average blood sugar level.
Whether to choose a 1-tailed test or a 2-tailed test in the given study would depend on the desired level of significance. If a directional hypothesis is present, then a 1-tailed test would be used.
However, in the absence of any such directional hypothesis, a 2-tailed test is used.
In the given study, we don't have a directional hypothesis; thus, we would use a 2-tailed test.
In general, the standard alpha value that is used in most statistical tests is 0.05.
So, in this study, we can also choose 0.05 as the significance value (alpha).
The steps that one would go through to test this hypothesis statistically are:
1. State the null and alternative hypothesis.
2. Choose the level of significance (alpha).
3. Collect data and calculate the sample mean and sample standard deviation.
4. Calculate the t-test statistic.
5. Determine the degrees of freedom (df).
6. Determine the p-value.
7. Compare the p-value with the level of significance (alpha).
8. If p-value ≤ alpha, reject the null hypothesis; otherwise, fail to reject the null hypothesis.
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There are 5 people in Edgar’s family
Answers
Answer:
3 wholes. Each member will get 3/5 of a loaf.
Step-by-step explanation:
3 ÷ 5 = 3/5
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5. Which of the following could represent the side
lengths of a triangle?
Check all that apply.
19, 11, 17
23, 28, 52
34,9, 25
13, 22, 14
Answers
Answer: 19,11,17 and 13,22,14
Step-by-step explanation:
The two smallest numbers (11, 17) added together must be a bigger number than the biggest number (19)...... 11 + 17 = 28
28> 19 :)
What kind of wear would you expect the femoral stem of a hip implant to most likely to suffer? Adhesive wear Oxidative O Oxidative O Fatigue O Corrosive O Fretting-corrosive Erosive O Fretting O Abrasive O Cavitation
Answers
The femoral stem of a hip implant is most likely to suffer from abrasive wear.
The femoral stem of a hip implant is likely to suffer Abrasive wear. Abrasive wear refers to the loss of material from the surface of a solid body by the motion of a harder material across this surface. The material loss is caused by the hard abrasive particles such as bone cement debris or particles from the surface of the implant.
Abrasive wear occurs due to friction, scratching, or rubbing. In a hip implant, this occurs when the femoral stem is rubbing against the acetabular cup, or in other words, the ball of the femoral stem rubs against the hip socket. The high forces generated during normal hip joint movement lead to this type of wear.
The type of wear that affects the femoral stem of a hip implant can cause damage to the implant over time, leading to implant failure. Some of the common factors that can lead to abrasive wear include implant misalignment, improper material selection, or the use of the implant beyond its recommended lifespan.
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Congruent angle pairs : Find m
Answers
Answer:
75
Step-by-step explanation:
x+60 and 5x are vertical angles, which means they are equal
x+60 = 5x
Subtract x from each side
x+60-x = 5x-x
60 = 4x
Divide by 4
60/4 = 4x/4
15 =x
We want to find x+60
x+60
15+60
75
Answer:
∠GH = 75°
Step-by-step explanation:
x + 60° = 5x° ( vertical angles )
subtract x from both side
x - x + 60° = 5x - x
60° = 4x
divide each side by 4
60°/ 4 = 4x / 4
15 ° = x
To calculate, ∠GH
∠GH = x + 60 °
15 ° + 60° .. ( x = 15°)
= 75°
lim x approaches infinity (2x-1)(3-x)/(x-1)(x+3) is
Answers
The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.
To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:
\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)
Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:
0 * 0 = 0
Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.
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