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2 years ago

Maximum value of P+4x+5y+21 given the following: y-x<1, 21x+7y<25, x>-2, y>-4

Mathematics

1 answer:

allsm [11]2 years ago

6 0

The maximum value of the objective function is 31.787

<h3>How to maximize the function?</h3>

The given parameters are:

Objective function:

Max P = 4x + 5y + 21

Subject to:

y- x < 1

21x + 7y < 25

x>-2, y>-4

Rewrite the inequalities as equation

y - x = 1

21x + 7y = 25

Add x to both sides in y - x = 1

y = x + 1

Substitute y = x + 1 in 21x + 7y = 25

21x + 7x + 7 = 25

Evaluate the like terms

28x = 18

Divide both sides by 28

x = 0.643

Substitute x = 0.643 in y = x + 1

y = 0.643 + 1

y = 1.643

So, we have:

Max P = 4x + 5y + 21

This gives

P = 4 * 0.643 + 5* 1.643 + 21

Evaluate

P = 31.787

Hence, the maximum value of the objective function is 31.787

Read more about maximum functions at:

brainly.com/question/14381991

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Given:

Total number of problems = 24

Michael completed $\dfrac{1}{4}$ of his homework in $\dfrac{3}{4}$ of an hour.

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Part of work done in $\dfrac{3}{4}$ of an hour $=\dfrac{1}{4}$

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2 years ago

Select the point that is a solution to the system if inequalities yx^2-6

labwork [276]

Answer:

The correct answer is A.

$A(0,-2)$

Step-by-step explanation:

Method 1

You just have to plot each point on the graph.

The one that falls within the solution region is the correct choice.

From the graph, $A(0,-2)$ falls within the solution region.

See graph

Method 2

If you substitute the points into the inequalities, the only point that will satisfy both inequalities simultaneously is A.

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$y\:$

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This statement is true.

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3 years ago

Paul bought 18 pins for $90. Jack bought 45 pins for $180. Who bought pins at the lowest cost?

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3 years ago

Read 2 more answers

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

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3 years ago