Monopoly Profit Maximization

The table below provides partial information for Putrid Gas & Electric, a monopoly operat the northwestern United States. The executives at Putrid would not divulge any more infor than given in this table, so it is up to you to fill in the holes. Complete the table and use it answer the questions that follow. $($The output is electricity in thousands of kilowatt hours.

$\backslash$table$[[$Output$,$Price,TR$,$MR$,$TC$,$ATC,MC$,$Profit$],[0,xxx,,x,110,x,xxx,],[1,,,90,,$$$144,,],[2,,,,,,29,-3],[3,80,,,,,,42],[4,,300,,,56\mathrm{.}75,,],[5,,,,261,,,89],[6,,,40,301,,,]]$

One or two numbers are positive, zero, or negative

Numbers Occurring Only Once

$q,$

Question $38$ Let's assume all numbers except two occur twice in an array. How do you get those two numbers to occur only once in $O(n)$ time and $0(1)$ space?

For example, only two numbers, $4$ and $6,$ in the array $\{2,4,3,6,3,2,5,5\}$ occur once, and the others numbers occur twice. Therefore, the output should be $4$ and $6.q,$

This is a very difficult interview question. When an interviewer notices that a candidate does not have any ideas after a few minutes, it is possible for the interviewer to modify the question a little bit: If all numbers except one occur twice in the array, how do you find the only number occurring only once? Why does the interviewer emphasize the times a number occurs $($once or twice$)?$ It reminds us Why does the interviewer emphasize the times a number occurs $($once or twice$)?$ It reminds us of the haracteristic of the bitwise XOR operation it gets $1$ when two input bits are different and gets $0$ when they are same. Therefore, XOR gets $0$ on a pair of duplicated numbers. If numbers in an array where all numbers except one occur twice are XORed, the resuls is exactly the number occurring only once. With the simplified problem solved, let's return back to the original one. We know how to solve it if we could partition the array into two sub$-$arrays, where only one number appears once and the others we could partition the array into two sub$-$arrays, where only one num. Supposing the two numbers occurring once in the array are num $1$ and num$2.$ If we take XOR operations on all numbers in the array, the result should be the same as the result of num$1^$num

$105$