Answer:
If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:
The restriction for cloth can be written as:
The restriction for metal can be written as:
The restriction for wood can be written as:
The condition for S and H to be positive is:
Step-by-step explanation:
We have an objective function that, in this case, we want ot maximize.
This function is the Profit (P).
If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:
We have 3 restrictions, plus the condition that both S and H are positive.
The restriction for cloth can be written as:
The restriction for metal can be written as:
The restriction for wood can be written as:
The condition for S and H to be positive is:
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
<h3>What are the hypothesis tested?</h3>At the null hypothesis we test if the means are equal, hence:
At the alternative hypothesis, it is tested if they are different, hence:
For each sample, they are given as follows:
Hence, for the distribution of differences, they are given by:
The test statistic is given by:
In which is the value tested at the null hypothesis.
Hence:
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/13873630
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