The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0). What are the minimum and maximum values of the objective function F = 8x + 5y?
Answers
The minimum and maximum values of the objective function f = 8x + 5y are 400 and 960
How to determine the minimum and the maximum values?The vertices of the feasible region are given as:
(0, 100), (0, 80), (80, 60), (80, 0), and (120, 0)
The objective function is given as:
z = 8x + 5y
Calculate the value of the objective function using the vertices
F = 8 * 0 + 5 * 100 = 500
F = 8 * 0 + 5 * 80 = 400
F = 8 * 80 + 5 * 60 = 940
F = 8 * 80 + 5 * 0 = 640
F = 8 * 120 + 5 * 0 = 960
The minimum value above is 400 and the maximum value is 960
Hence, the minimum and maximum values of the objective function F = 8x + 5y are 400 and 960
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Related Questions
What is the markup for a pair of hiking boots that the store buys for $80 each if the markup rate is 15%?
Answers
Final answer:
To find the markup on a pair of hiking boots with a cost of $80 and a 15% markup rate, multiply the cost by 0.15 to get a $12 markup. The selling price would then be $80 + $12, totaling $92.
Explanation:
To calculate the markup for a pair of hiking boots that the store buys for $80 with a markup rate of 15%, first convert the percentage to a decimal by dividing by 100.
Markup rate as a decimal: 0.15
Next, multiply the cost price by the decimal.
Markup amount = Cost price × Markup rate
Markup amount = $80 × 0.15
Markup amount = $12
So, the markup on the hiking boots is $12. To find the selling price, you add the markup to the cost price:
Selling price = Cost price + Markup amount
Selling price = $80 + $12
Selling price = $92
The store would sell the hiking boots for $92.
A 3x3x4 cuboid is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?
Answers
A 3 x 3 x 4 cuboid can be cut into 3(3) (4) = 36 pieces of 1 x 1 cubes.
Out of the 36 pieces of 1 x 1 cubes, there are no 1 x 1 cube with the four
sides painted, there are eight 1 x 1 cubes with simply 3 sides painted, there
are twenty 1 x 1 cubes with only 2 sides tinted, there are 6 cubes with only 1
side painted and there are 2 cubes with no side painted.
The chance that the four sides of a randomly selected cube is painted is 0.
The likelihood that only 3 sides of a randomly selected cube is painted is 8 / 36 = 2 / 9.
The chance that only 2 sides of a randomly selected cube is painted is 20 / 36 = 5 / 9.
The likelihood that only 1 side of a randomly selected cube is painted is 6 / 36 = 1 / 6.
The probability that no side of a randomly selected cube is
painted is 2 / 36 = 1 / 18.
Thus, the expected value for the painted sides of a randomly selected cube is
given by 4(0) + 3(2 / 9) + 2(5 / 9) + 1(1 / 6) + 0( 1 / 18) = 2 / 3 + 10 / 9 +
1 / 6 = 35 / 18 = 1.94
Agnes scored 87 on the first test 73 on the second test, 81 on the third test. supoise Agbes has one more test in the semester ajd wants to finish with a mean of at least 80. what does she need to get on her last test?
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How do I use the info given in the table to figure out the answers?
Answers
You can do this as direct proportion problem.
The number of gallons filled is proportional to the number of hours, and the rate of filling is:
rate = number of gallons / number of hours
From the two data in the second column you have:
number of hours = 3/4 h = 0.75 h
number of gallons = 637 + 1/2 gallons = 637.5 gallons
=>rate = 637.5 gal / 0.75 h = 850 gal/h
In the second column you have the number of hours and want to find the number of gallons, so assuming direct proportionality:
number of hours = 1/4 = 0.25
rate = 637.5 / 0.75 = x / 0.25
=> x = 0.25 * rate = 0.25 h * 850 gal/h = 212.5 gallons.
And from the third column:
number of hours = 1 + 1/2 hours = 1.5 hours
rate = x / 1.5 => x = 1.5h * rate = 850gal/h * 1.5h = 1275 gallons
With that you have already solved a. and b.
You should know how to answer c. and d. This is how:
c. number of gallons = 5.5 hours
number of gallons = rate * number of hours = 850 gal/h * 5.5 h = 4675 gal.
d. number of gallons = 100 gal
rate = 100 gal / number of hours => number of hours = 100 gal / rate
=> number of hours = 100 gal / 850 gal/h = (2/17) h
Pass to minutes => (2/17) h * 60 min/h ≈ 7 min
Solve for A, 4(2a+3)=-3(a-1)+31
Answers
Step 1: Simplify both sides of the equation.4(2a+3)=−3(a−1)+31(4)(2a)+(4)(3)=(−3)(a)+(−3)(−1)+31(Distribute)8a+12=−3a+3+318a+12=(−3a)+(3+31)(Combine Like Terms)8a+12=−3a+348a+12=−3a+34Step 2: Add 3a to both sides.8a+12+3a=−3a+34+3a11a+12=34Step 3: Subtract 12 from both sides.11a+12−12=34−1211a=22Step 4: Divide both sides by 11.11a1/1=22/11
the answer is a=2
What's the value of the 8's in 88,000
Answers
What is the equation of the line that goes through (3,11) and is parallel to the line 2x-y=5
Answers
why?
2x-y=5
y=2x-5
from here we can find the slope, which is 2, and we know that parallel lines have equal slopes
the standard form of eq of line is y=mx+b
substitute y and x with the numbers from ordinate pair (3,11):
11=3*2+b
6+b=11
b=5
Now you can write the eq of line:
y=2x+5
Suppose you randomly select a letter from BURGER AND STARBIRD. Imagine writing these letters on Ping- Pong balls—one letter per ball—then putting them all in a barrel and remov- ing one. What is the probability of pulling out an R?
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Hope this helps!
867,000 rounded to the nearest hundred thousand
Answers
Round 992,449 to the nearest hundred thousand
Answers
hope this helps
You have a 5 question multiple choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?
Type your answer below using complete sentences.
Answers
p = 1/4. the probability of guessing a correct answer.
q = 1 - p = 3/4, the probability of guessing a wrong answer.
The probability of guessing 3 out of 5 questions is
[tex]_{5}C_{3} \,p^{3}q^{5-3} = \frac{5!}{3!2!}( \frac{1}{4})^{3}( \frac{3}{4})^{2} = 0.088[/tex]
Answer: 0.088
how do i solve 2 1/7 ÷ 1 1/4
Answers
2 1/7= 15/7.
1 1/4= 5/4
To divide fractions, multiply the first number by the reciprocal of the other. To multiply fractions, multiply the numerators and the denominators together.
(15/7)* (4/5) = 60/35
60/35= 12/7
Final answer: 12/7 or 1 5/7
(2.03)
Below are the steps to solve an equation:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
Which of the following is a correct next step to solve the equation? (1 point)
Answers
Rember that |x| = x when x is positive and |x| is - x when x is negative.
So, these are the two possibilities for |x - 2| = 4
1) When the content inside the absolute value is positive, you can state x - 2 = 4
2) When the content inside the absolute value is negative you can state x - 2 = - 4.
So, the answer is
x - 2 = 4 and x - 2 = - 4.
I found this list of choices for this question:
a. x + 2 = −4
b. −x − 2 = 4
c. x + 2 = 4
d. x − 2 = −4
In that list , the only right is x - 2 = - 4, so choose it.
Answer: option d. x - 2 = - 4
For questions #6-8, use this data set and show your work 5, 10, 12, 4, 6, 11, 13, 5
Calculate the mean.
Type answer here
Calculate the median.
Type answer here
Calculate the mode.
Answers
(5+10+12+4+6+11+13+5) / 8 = 66/8 = 8.25 <==
the mode (the number used most often) = 5....just so u know, there doesn't have to be a mode, and sometimes there is more then 1 mode. But for this one, the mode is 5. <==
median (the middle number)...for this, u put the numbers in order...
4,5,5,(6,10),11,12,13
now start moving from both ends going inward until u find the middle number...keep in mind, when u have an odd number of numbers, u will have 1 middle number.....but when there is an even number of numbers, like in this case, u will have 2 middle numbers...so u take ur 2 middle numbers, add them, then divide by 2 to get ur median.
median = (6 + 10) / 2 = 16/2 = 8 <==
is math related to science ?
Answers
The table shows the cost of a ski rental package for a given number of people. People Cost ($) 4 160 5 200 6 240 7 280 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. A. 1/40 dollars per room; the cost is $40 for each person. B. 40/1 dollars per person; the cost is $40 for each person. C. 1/280 dollars per person; the cost is $1 for 280 people. D. 160/1 dollars per person; the cost is $160 for each person.
Answers
Thanks (:
The answer is B. 40/1 dollars per person; the cost is $40 for each person.
A coffeepot contains 1 1/2 quqarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1/2 cups of coffee still remain in the pot. How much coffee did Tonya pour into each cup?
Answers
[tex]\bf \textit{now if }\frac{3}{8}\textit{ of coffee makes }5\frac{1}{2}\textit{ cups, how much in 1 cup?} \\\\\\ \cfrac{\quad \frac{3}{8}\quad }{5\frac{1}{2}}\implies \cfrac{\quad \frac{3}{8}\quad }{\frac{5\cdot 2+1}{2}}\implies \cfrac{\quad \frac{3}{8}\quad }{\frac{11}{2}}\implies \cfrac{3}{8}\cdot \cfrac{2}{11}\implies \stackrel{\textit{of coffee makes one cup}}{\cfrac{3}{44}}[/tex]
290 in expanded notation
Answers
This is the answer. 200 + 90 + 0
The place value chart can help us to write a number in expanded notation. When we put 290 into the place value chart, we can recognize that our number is equal to
2 hundreds + 9 tens + 0 units
Image is provided.
Alan is 14 years old. This is twice as old as his brother James. How old is James?
Answers
James is 7.
alan is twice as old as his brother
alan=2 times brother
14=2 times brother (james)
divide both sides by 2
7=brother (james)
james is 7 years old
what is 8x-27-10-6x=15
Answers
2x-37=15
2x=15+37
2x= 52
x=26
2x - 37 = 15
Then, add 37 to each side to get:
2x = 52
Lastly, divide each side by 2 to get:
x = 26
Hope this helps!! :)
The nurse researcher is reading about linear regression. what is linear regression
Answers
Linear regression is a useful tool that allows calculating approximate values for a function that passes through given points(with the best error possible). It is very useful in science to make an estimation of the comportment of movement, electricity and some decays.
For example, I will relate a case in a physics lab: We calculated the positions of a car in an air rail and the times. With this information, I was able to make a linear regression to calculate the Position function for that case.
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground. NextReset
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Answer:
The bird is at a height of 1.95 km from the ground.
Step-by-step explanation:
It is given that the distance between susan and mark is 7 km and bird is between susan and mark. The angles of elevation they make are 20º and 50º, respectively.
Draw a perpendicular line from the bird on base.
Let the distance of susan from and the altitude be x.
In triangle ABS,
[tex]tan(20^{\circ})=\frac{AB}{x}[/tex]
[tex]tan(20^{\circ})x=AB[/tex]
[tex]0.364x=AB[/tex] ..... (1)
In triangle ABM,
[tex]tan(50^{\circ})=\frac{AB}{7-x}[/tex]
[tex]1.192(7-x)=AB[/tex] ..... (2)
From (1) and (2), we get
[tex]0.364x=1.192(7-x)[/tex]
[tex]1.556x=8342[/tex]
[tex]x=5.36[/tex]
The length of AB is,
[tex]AB=0.364(5.36)=1.95147\approx 1.95[/tex]
Therefore, the he bird is at a height of 1.95 km from the ground.
Connor drives an an eighteen-wheeler. It cost Conner $456 to fill the truck up with diesel fuel. If diesel fuel cost $3 a gallon, how many gallons of fuel were bought?
Answers
What is 45122 to the nearest ten thousand
Answers
There are two lakes in town of Roxbury. Lake Big Rock is 1650 ft longer than Little Lake Rock. Together, they are 5273 ft long. How long is each lake? Please show work.
Answers
then then subtract 1650 form your answer which = 1973 so the first lake is 3623 ft long and the second is 1973 ft long. hope this helps.
Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.
Let's use algebra to solve this problem.
Let L be the length of Little Lake Rock in feet, and let B be the length of Lake Big Rock in feet.
We are given two pieces of information:
Lake Big Rock is 1650 ft longer than Little Lake Rock: B = L + 1650.
Together, they are 5273 ft long: B + L = 5273.
Now, we have a system of two equations with two variables:
B = L + 1650
B + L = 5273
We can use the first equation to express B in terms of L and then substitute this expression into the second equation:
B = L + 1650
Now, substitute B in the second equation:
(L + 1650) + L = 5273
Combine like terms:
2L + 1650 = 5273
Subtract 1650 from both sides:
2L = 5273 - 1650
2L = 3623
Now, divide by 2 to find the length of Little Lake Rock (L):
L = 3623 / 2
L = 1811.5 feet
Now that we know the length of Little Lake Rock, we can find the length of Lake Big Rock using the first equation:
B = L + 1650
B = 1811.5 + 1650
B = 3461.5 feet
So, Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.
for such more question on length
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The sum of the square of a positive number and the square of 5 more than the number is 37. What is the number?
Answers
x^2 + (x+5)^2 = 37
Expanding, x^2+x^2+10x +25=37, or 2x^2+10x-12=0.
Reducing, x^2+5x-6=0. factoring, (x-1)(x+6)=0
Solving for x: x-1=0 results in x=1; x=6=0 results in x=-6.
We want only a positive result, so choose x=1 and discard x=-6.
A student measured the lead content of a paint sample 4 times. the standard deviation of the measurements was found to be 1.1% of the average. can this student be 90% confident that the true value is within 1.8% of the measured average?
Answers
Multiply and simplify -12i x 3i
Answers
12×3=36 i×i=i²
So in the case of basic algebra, it's 36i²
If i is √-1 then i² is √-1×√-1 which is -1
36×-1=-36
At a wedding reception, the bride and groom and five attendants will form a receiving line. How many ways can they be arranged in each of following cases? a) Any order will do. b) The bride and groom must be the last two in line. c) The groom must be last in line with the bride next to him.
Answers
A. In this case, they can be arranged at any order. Since there are 7 people all in all, therefore the number of arrangements is:
number of arrangements = 7P7 = 5040 ways
B. In this case, only the 5 people can be arranged in any order therefore 5P5. However the groom and bride can be interchanged on 2 places, therefore:
number of arrangements = 5P5 * 2 = 240 ways
C. In this case, only the 5 people can be arranged in any order while the groom and bride can no longer be interchanged, therefore:
number of arrangements = 5P5 = 120 ways
Final answer:
The arrangements for the wedding reception receiving line can be calculated using permutations: a) Any order will do, giving 7!, b) The bride and groom must be the last two in line, giving 5!, c) The groom must be last in line with the bride next to him, giving 6! x 2.
Explanation:
The question asks about the number of ways a bride and groom along with five attendants can be arranged in a receiving line at a wedding reception under different conditions. This is a permutations problem where we calculate the arrangements using factorial notation.
Case a: Any order will do.
In this case, we have a total of 7 people (bride, groom, and five attendants) who can be arranged in any order. The number of arrangements is the factorial of 7, which is calculated as 7! (7 factorial). So, the number of ways they can be arranged is 7! (which is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 ways).
Case b: The bride and groom must be the last two in line.
Since the bride and groom's positions are fixed at the end of the line, we only need to arrange the five attendants. This is equivalent to 5! arrangements for the attendants. Thus, the number of ways they can be arranged is 5! (which is 5 x 4 x 3 x 2 x 1 = 120 ways).
Case c: The groom must be last in line with the bride next to him.
Here, the bride and groom are fixed in the last two positions, but the bride must be next to the groom. We consider the bride and groom as a single unit in addition to the five attendants. This gives us 6! arrangements for the attendants and the bride-groom unit, multiplied by 2 because the bride and groom can switch places within their unit. So, the number of ways they can be arranged is 6! x 2 (which is 6 x 5 x 4 x 3 x 2 x 1 x 2 = 1,440 ways).
Figure ABCD is a parallelogram. What is the value of n?
3
5
17
25
Answers
2n + 32 = 4n - 2
34 = 2n
n = 17 answer
Answer: the answer to this question is
choice c. 17