Solve the linear programming problem.
Maximize
P=40x + 50y
Subject to
2x+y ≤ 14
x+y ≤ 8
x + 2y ≤ 12
x, y 20
Answers
Answer:
x = y = 4
Step-by-step explanation:
A 2-variable linear programming problem is nicely solved by graphing. The solution will be one of the vertices of the solution set. The attached graph shows that means it is one of (x, y) = [(0, 0), (0, 6), (4, 4), (6, 2), (7, 0)}.
__
Evaluating the objective function at each of these vertices will show you the solution that maximizes it.
(0, 0) -- P = 40·0 +50·0 = 0
(0, 6) -- P = 40·0 +50·6 = 300
(4, 4) -- P = 40·4 +50·4 = 360
(6, 2) -- P = 40·6 +50·2 = 340
(7, 0) -- P = 40·7 +50·0 = 280
_____
Additional comment
The solution set would ordinarily be the area that is covered by the shading that signifies the solution set of each of the 5 inequalities. 5 different overlapping shadings can make the graph quite messy, so we have elected to shade the areas that are NOT part of the solution set. In doing so, we have made the boundary lines dashed when they are part of the solution set
The possible solutions are the vertices of the white space on the graph.
The black line on the graph is the line corresponding to the maximum value of the objective function. To maximize the objective function, we want that line as far from the origin as possible. It is shown intersecting the vertex of the solution space that meets that condition.
Related Questions
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles faster than the other. If the two buses are 640 miles apart after 5 hours, what is the rate of each bus?
Answers
If the two buses are 640 miles apart after 5 hours. Then the rate of each bus will be 57 miles per hour and 71 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Two buses leave a station at the same time and travel in opposite directions.
One bus travels 14 miles faster than the other.
Let x be the speed of first bus. Then the speed of the second bus will be (x + 14).
If the two buses are 640 miles apart after 5 hours.
Then the rate of each bus will be
Then the relative speed of the buses will be
S = x + x + 14
S = 2x + 14
Then the value of x will be
2x + 14 = 640 / 5
2x + 14 = 128
2x = 114
x = 57 miles per hour
Then the speed of the other bus will be
⇒ 57 + 14
⇒ 71 miles per hour
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ1
From this diagram, select the
pair of lines that must be
parallel if angle 1 is congruent to angle 8. If there is no pair of lines, select "none".
Answers
Answer:
Line L is parallel to Nangle 1 is equal to angle 4 ( vertically opposite angles)
if angle 1 is congruent to angle 8
then angle 4 is also congruent to angle 8
then slope of line L and n is equal
that is L is parallel to n
What negative Z-score (standard score) would the area under the curve be 0.8621
z* = _______
Answers
Name all the fractions that are between 12/13 and 19/20
whose NUMERATORS are one less than the DENOMINATORS.
Answers
The fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Fractions that are between 12/13 and 19/20 such that:
The numerator(N) is one less than the denominator(D).
N = D - 1
N = (12, 19)
D = (13, 20)
D = 14, N = 13
D = 15, N = 14
D = 16, N = 15
D = 17, N = 16
D = 18, N = 17
D = 19, N = 18
The fractions that are between 12/13 and 19/20:
N/D = {13/14, 14/15, 15/16, 16/17, 17/18, 18/19}
Thus, the fractions that are between 12/13 and 19/20 are 13/14, 14/15, 15/16, 16/17, 17/18, and 18/19 total number of fractions is 6
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ1
evaluate this exponential expression 5 • (3 + 6)^2 - 6^2
Answers
The answer of this expression is 369
We know that to solve a numerical expression, we will calculate with property base form.
When there are symbols in an expression, we first solve the numbers in order that are between:
Parentheses ( ) Brackets [ ] Braces { }The math signs calculated first in order are;
Power - square root Multiplication - divisionAddition - subtractionGiven the expression, the resolution will be:
5 * ( 3 + 6 )² - 6²
5 * 9² - 6²
5 * 81 - 36
406 - 36
369
So, the value of this numeric expression is 369
paul asked to order snacks for an office meeting of 180 people. she decides to order desert squares which come in boxes of 24. she estimates she will need 3.5 snacks per person. how many boxes should she buy?
Answers
Answer:
27 boxses
Step-by-step explanation:
calculations is shown in the picture
What is the value of the expression 24 + 3²? What is the value of the expression 24 + 3² ?
Answers
Answer:
33
Step-by-step explanation:
3² = 3.3 = 9 => 24 + 9 = 33
Mrs. Avery is going to randomly select one student from her class to read a poem out loud. There are 151515 boys and 131313 girls in her class.
What is \text{P(boy})P(boy)start text, P, left parenthesis, b, o, y, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
Answers
The probability that a boy is selected is 0.5357 or 53.57%
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
P(boy) is asking for the probability that a boy will be chosen to read a poem out loud. Since there are 15 boys, we can get the probability by dividing this by the total number of students.
This is because out of all the students, there is an equal possibility that each of the 15 boys will be chosen.
P = ( 15 ) / ( 15+13)
P = 15 / 28
P = 0.5357
Therefore the probability that a boy is selected is 0.5357 or 53.57%
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
Answer:
53.57%
Step-by-step explanation:
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
Answers
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
To learn more about the Z score, refer to;
https://brainly.com/question/15016913
#SPJ1
A researcher conducts an between-subjects study examining the
effectiveness of a memory enhancement program at an assisted living
facility for elderly adults. One group of residents is selected to
participate in the program, and a second group of participants serves as
a control group. After 6 weeks, the researcher reports a combined score
measuring memory for each individual. The data are:
Control
Exercise
n = 10
M = 12
SS = 120.5
n=15
M= 15.5
SS = 190.0
a) Does the exercise program have a significant effect? Use a two
tailed test with an alpha level of .05
b) Compute Cohen's d to measure the size of the treatment effect
Answers
H0: µ1 = µ2; The exercise program do not have significant effect on physical fitness, H1: µ1 =/ µ2; the exercise program had a significant effect on physical fitness and the Estimated Cohen's d is 0.82.
HypothesisA. Significant effect
H0: µ1 = µ2
Based on the above hypothesis the exercise program does not have significant effect on physical fitness
H1: µ1 =/ µ2
Based on the above hypothesis the exercise program had a significant effect on physical fitness
Pooled variance: sp2 = (190 + 120.5/(15-1) + (10-1)
Pooled variance: sp2 = 310.5/23
Pooled variance: sp2 =13.5
Estimated standard error ( sM1-M2):
sM1-M2 =√13.5/15 +13.5/10
sM1-M2 =√2.25
sM1-M2 = 1.5
Tailed test (t)
t = (15.5 - 12)/1.5
t=3.5/1.5
t= 2.33
B. Estimated Cohen's d:
Estimated Cohen's d = 3/√13.5
Estimated Cohen's d = 3/3.67
Estimated Cohen's d= 0.817
Estimated Cohen's d= 0.82 (Approximately); this is a large effect.
Conclusion demonstrating how the outcome of the hypothesis test would tend to appear in a research report is: (Reject H0). Because the group exercise program tend to have a significant effect on the physical fitness of elderly adults, t = 2.33, p <.05, d = 0.82.
Learn more about hypothesis here:https://brainly.com/question/15980493
https://brainly.com/question/14042255
#SPJ1
Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.
Answers
The equation in terms of t that models the situation is given by
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].
We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as
[tex]A = P(1+\frac{r}{n})^{nt}[/tex],
where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.
Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710
So, we can write
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Therefore the required equation is
[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]
Know more about compound interest here -
https://brainly.com/question/13870442
#SPJ10
ING DROPS
1. The total volume to be given is 30 ml.
The time over which this is to be given is 30 minutes.
The drop factor is 15.
How many drops per minute will be delivered ?
Answers
Answer:
15 drops per minute
Step-by-step explanation:
(drops per minute) flow/drip rate: volume ÷ time × drop factor
note:
volume (mL)
time (minutes)\
30 / 30 = 1
1 * 15 = 15
so, 15 drops per minute will be delivered
hope this helps!! have a lovely day :)
Answer:
15 drops/minute
Step-by-step explanation:
30 ÷ 30 = 1
1 · 15 = 15
hope this is helpful :)
What are m and b in the linear equation 3+4x+6+2x=y
Answers
Answer:
m = 6, b= 9
Step-by-step explanation:
Simplifying the equation, we get y = 6x + 9.
Matching this up with y = mx + b, we get m = 6 and b = 9.
Translate the phrase; then simplify. Find the sum of −45, −13, and 37.
Answers
Answer:
-21
Step-by-step explanation:
37 - 45 - 13 is translated
-8 - 13
-21
determined about the triangle formed by the ground,
wall, and ladder? Check all that apply.
The triangle is isosceles.
The leg-to-hypotenuse
ratio is 1:√√2.
The leg-to-hypotenuse ratio is 1:√2.
The nonright angles are congruent.
The ladder represents the longest length in the
triangle.
(A,B,D,E)
Answers
Answer:
a² b² c² equals mc² and that is the answer
Solve the following subtraction problem. Remember to borrow as necessary.
9cu yd113cu in
− 4cu ft129cu in
−−−−−−−−−−−−−−−−−−−−−−
Answers
The subtraction of the expression will be 238 cubic feet, 551 cubic inches.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in
1 cubic yard = 27 cubic feet
1 cubic feet = 1728 cubic inches
Then the subtraction will be
242 cu ft 1841 cu in
− 4 cu ft 1290 cu in
238 cu ft 551 cu in
More about the subtraction link is given below.
https://brainly.com/question/4319655
#SPJ1
Which expression is equivalent to...
Answers
Answer:
A is correct yes
Step-by-step explanation:
ndnanndnqnjed
The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.
{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)
Answers
The correct representations of this solution are
(d) A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.(e) (3, ∞)How to determine the solution set?The inequality is given as:
6 + 2n > 12
The solution is given as:
n > 3
When the above inequality is represented as an interval, we have:
(3, ∞)
Also, the inequality symbol > is represented using an open circle.
This means that the number line would use an open circle and the arrow would point right
Hence, the correct representations of this solution are (d) and (e)
Read more about inequalities at:
https://brainly.com/question/25275758
#SPJ1
Find the solutions to the equation below. check all that apply. x^2-2x-15=0
Answers
The student did not make any mistake, the solution is correct. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A student perform the following steps to find the solution of the equation x² – 2x – 15 = 0.
The factor of the equation will be
Step 1 : x² – 2x – 15 = (x – 5)(x + 3)
Step 2 : (x – 5) = 0 and (x + 3) = 0
Step 3 : x = 5 and – 3
The student did not make any mistake, the solution is correct.
Then the correct option is A.
More about the factorization link is given below.
https://brainly.com/question/6810544
#SPJ1
Which of the numbers below are whole numbers? Check all that apply.
A. 6830
B. 66
C. 717.59
D. 808
E. 42.3
F. 1/10
Answers
Step-by-step explanation:
Anything which has a decimal point is not a whole number
6830 is
66 is
717.59 is not
808 is
42.3 is not
1/10 = 0.1 ergo is not
Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answers
Answer:
12
Step-by-step explanation:
1.5 is 1 1/2 in decimal form
1.5×8=12
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f- g)(x).
Answers
Step-by-step explanation:
please mark me as brainlest
f is an even function, g is an even function. a=
Answers
Answer:
a=6 it's even
Step-by-step explanation:
please mark me as brainlest
Answer:
A= 4
B= 3
i got it right.
What is the answer to this question?
Y=x^2-1 with the input as 5
Answers
We can see that, when the input is 5, the output is 24.
How to evaluate an equation?
Here we have the equation:
[tex]y = x^2 - 1[/tex]
Where y is the output and x is the input.
We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:
[tex]y = 5^2 - 1 = 24[/tex]
Then we can see that, when the input is 5, the output is 24.
If you want to learn more about evaluating functions:
https://brainly.com/question/1719822
#SPJ1
Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
Answers
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
Learn more about function sum;
https://brainly.com/question/14438192
#SPJ1
a plane intersects a sphere 5 cm away from the center of the sphere. the cross section is a circle whose diameter is 12cm. determine the radius of the sphere
Answers
Answer:
7.81 cm
Step-by-step explanation:
diameter = 12, 12/2 = 6
(r+5)(r-5) = 6 * 6
r^2 - 25 = 36
r^2 = 61
r = 7.81
radius = 7.81 cm
Answer:
26
Step-by-step explanation:
QUESTION 8 - 1 POINT
The median monthly rent in 1994 was $499 and $633 in 2001. What was the percent increase in the
median monthly rent prices from 1994 to 2001? Round to the nearest tenth of a percent.
Answers
Answer:
26.85%
Step-by-step explanation:
first you find the difference in price increase
633-499=134
*percentage increase=increase value/original value x100
so;=134/499x100=28.85%
hope it helps you.please don't forget to give me a thanks
How much would it cost to buy a piece of candy for 50 cents plus tax
Answers
Answer:
it depends on which state your in or in your even in the us usually it is either 6% or 4% some times more or less % so im going to do both
50*0.06=53
50*0.04=52
Hope This Helps!!!
What is the range of the function represented by the following graph?
*
1 point
Captionless Image
A. all real numbers greater than 4
B. all real numbers less than - 1
C. all real numbers greater than - 6
D. all real numbers less than - 4
Answers
Answer:
C the prove is right there on the graph
Answer:
C
Step-by-step explanation:
The graph clearly shows that all the numbers are greater than -6
By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for sh.56 , gain is as much as percent as its cost in dollars . What is the cost price ?
Answers
The cost price of the table is $40.
What is Gain ?Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
To know more about Gain
https://brainly.com/question/23385214
#SPJ1
