Don’t mind the work but can someone please help fast I’m stuck!! I also need to show work
1 answer:
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Answer:
Maximum profit at (3,0) is $27.
Step-by-step explanation:
Let quantity of products A=x
Quantity of products B=y
Product A takes time on machine L=2 hours
Product A takes time on machine M=2 hours
Product B takes time on machineL= 4 hours
Product B takes time on machine M=3 hours
Machine L can used total time= 8hours
Machine M can used total time= 6hours
Profit on product A= $9
Profit on product B=$7
According to question
Objective function Z=
Constraints:
Where
I equation
I equation in inequality change into equality we get
Put x=0 then we get
y=2
If we put y=0 then we get
x= 3
Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I
Now put x=0 and y=0 in I equation in inequality
Then we get
Hence, this equation is true then shaded regoin is below the line .
Similarly , for II equation
First change inequality equation into equality equation
we get
Put x= 0 then we get
y=2
Put y=0 Then we get
x=4
Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II
Point A and C are same
Put x=0 and y=0 in the in inequality equation II then we get
Hence, this equation is true .Therefore, the shaded region is below the line.
By graph we can see both line intersect at the points A(0,2)
The feasible region is AOBA and bounded.
To find the value of objective function on points
A (0,2), O(0,0) and B(3,0)
Put A(0,2)
Z=
At point O(0,0)
Z=0
At point B(3,0)
Z=
Hence maximum value of z= 27 at point B(3,0)
Therefore, the maximum profit is $27.
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is , which is the pvalue of Z when X = 51.5 So
has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300