There is one critical point at (2, 4), but this point happens to fall on one of the boundaries of the region. We'll get to that point in a moment.
Along the boundary , we have
which attains a maximum value of
Along , we have
which attains a maximum of
Along , we have
which attains a maximum of
So over the given region, the absolute maximum of is 1578 at (2, 44).
Answer:
The 98% confidence interval for the mean purchases of all customers is ($37.40, $61.74).
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the mean subtracted by M. So it is 49.57 - 12.17 = $37.40.
The upper end of the interval is the mean added to M. So it is 49.57 + 12.17 = $61.74.
The 98% confidence interval for the mean purchases of all customers is ($37.40, $61.74).