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1 answer:
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Answer:
(x, y) = (3, 4.5)
Step-by-step explanation:
You want to find x and y such that xy is a maximum subject to the constraint that 3x+2y=18.
<h3>Objective function</h3>The objective function f(x, y) = xy is most easily maximized if it can be written in terms of one variable only. Solving the constraint equation for y, we have ...
3x +2y = 18
2y = 18 -3x
y = 1/2(18 -3x) = (3/2)(6 -x)
Then the objective function is ...
f(x) = x(3/2)(6 -x)
<h3>Maximum</h3>We recognize this as the equation of a parabola that opens downward, and has zeros at x=0 and x=6. Its line of symmetry is halfway between those, at x = 3. That is the location of the maximum of the objective function.
The corresponding y-value is ...
y = (3/2)(6 -3) = 9/2 = 4.5
The values of x and y that maximize their product are (x, y) = (3, 4.5).
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<em>Additional comment</em>
In the attached graph, the larger the product, the farther away the curve is from the origin. The product is maximized subject to the constraint when the curves are tangent to each other. That point of tangency is (x, y) = (3, 4.5).
Answer:
The required P value is 0.0901.
The critical value for the test statistic is 1.645.
Step-by-step explanation:
Consider the provided information.
The test statistic of z=1.34 is obtained when testing the claim that p> 0.1
It is given given that z=1.34 as the claim has greater than inequality so it is a right tailed test.
Part (A) P-value
From the Standard normal distribution table .
Therefore,
Hence, the required P value is 0.0901.
Part (B) The critical value(s) is/are z=
It is given that the significance level is α=0.05
Using standard z value table we get the critical value for the test statistic is 1.645.
Hence, the critical value for the test statistic is 1.645.