Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400.Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region.
c. What is the optimal solution?
Answers
Answer:
Let X1 be the number of decorative wood frame doors and X2 be the number of windows.
The profit earned from selling each door is $500 and the profit earned from selling of each window is $400.
The Sanderson Manufacturer wants to maximize their profit. So for this model, the objective function is
Max: 500X1 + 400X2
Now the total time available for cutting of door and window are 2400 minutes.
so the time taken in cutting should be less than or equal to 2400.
60X1 + 30X2 ≤ 2400
The total available time for sanding of door and window are 2400 minutes. Therefore, the time taken in sanding will be less than or equal to 2400. 30X1 + 45X2 ≤ 2400
The total time available for finishing of door and window is 3600 hours. Therefore, the time taken in finishing will be less than or equal to 3600. 30X1 + 60X2 ≤ 3600
As the number of decorative wood frame door and the number of windows cannot be negative.
Therefore, X1, X2 ≥ 0
so the questions
a)
The LP mode for this model is;
Max: 500X1 + 400X2
Subject to:
60X1 + 30X2 ≤ 2400
]30X1 +45X2 ≤ 2400
30X1 + 60X2 ≤ 3600
X1, X2 ≥ 0
b) Plot the graph of the LP
Max: 500X1+ 400X2
Subject to:
60X1 + 30X2 ≤ 2400
30X1 + 45X2 ≤ 2400
30X1 + 60X2 ≤ 3600
X1,X2
≥ 0
In the uploaded image of the graph, the shaded region in the graph is the feasible region.
c) Consider the following corner point's (0,0), (0, 53.33), (20, 40) and (40, 0) of the feasible region from the graph
At point (0, 0), the objective function,
500X1 + 400X2 = 500 × 0 + 400 × 0
= 0
At point (0, 53.33), the value of objective function,
500X1 + 400X2 = 500 × 0 + 400 × 53.33 = 21332
At point (40, 0), the value of objective function,
500X1 + 400X2 = 500 × 40 + 400 × 0 = 20000
At point (20, 40), the value of objective function
500X1 + 400X2 = 500 × 20 + 400 × 40 = 26000
The maximum value of the objective function is
26000 at corner point ( 20, 40 )
Hence, the optimal solution of this problem is
X1 = 20, X2 = 40 and the objective is 26000
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Please help, will mark you as brainleist!!!
situation. If a random sample of 25 people are selected from such a population, what is the
probability that at least two will be displeased?
A) 0.045
B) 0.311
C) 0.373
D) 0.627
E) 0.689
Answers
The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.
What is probability?
It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
This problem can be solved using the binomialdistribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).
Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).
Then, the probability of an individual not being displeased is:
1 - p = 0.955.
Let X be the number of displeasedpeople in a random sample of 25.
We want to find the probability that at least two people are displeased, which can be expressed as:
P(X ≥ 2) = 1 - P(X < 2)
To calculate P(X < 2), we can use the binomial distribution formula:
where n is the samplesize (25), k is the number of displeasedpeople, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.
For k = 0, we have:
≈ 0.378
For k = 1, we have:
≈ 0.42
Therefore,
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.
Finally, we can calculate,
P(X ≥ 2) = 1 - P(X < 2)
= 1 - 0.798
= 0.202.
Thus,
The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.
Learn more about probability here:
#SPJ2
Answer:
Step-by-step explanation:
The correct answer is (B).
Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.
P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.
P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.
Answers
Answer:
B and D
Step-by-step explanation:
To find the percentage, you divide Martin's correct answers by the total number of questions, then multiply the result by 100.
To find the fraction, it's correct answers/total questions.
Answer:
you should get your answer to be ,B and D
X
1 1 2 2 3 3 4
FX) -1 3 4 0 5 1 6
Label:
Explanation:
Answers
Answer:
Not a function
Step-by-step explanation:
Each input can have only have one output.
x(1) can't equal both -1 and 3 at the same time.
x(2) can't equal both 4 and 0 at the same time.
x(3) can't equal both 5 and 1 at the same time.
In other words there can't be multiple X's equalling different things.
Answers
Answer:
33 in
Step-by-step explanation:
The Pythagorean theorem tells you ...
diagonal² = length² +width²
diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²
diagonal = √(1068.25 in²) ≈ 32.684 in
The diagonal of the television is about 33 inches.
Answers
Answer:
L=10cm , W=30cm
Step-by-step explanation:
First use the given that W=10+2*L
Use P=2W+2L=80, substitute W in the perimeter formula
2(10+2L)+2L=80 and solve for L,
20+4L+2L=80 isolate variable L and combine like terms,
6L=80-20,
L=10, so W=10+2*10=10+20=30
Answers
Answer:
36 9/16 ft^3
Step-by-step explanation:
volume = length * width * height
volume = 3 3/4 ft * 3 ft * 3 1/4 ft
Change all mixed numerals to fractions.
volume = 15/4 * 3/1 * 13/4 ft^3
volume = 585/16 ft^3
volume = 36 9/16 ft^3