Combinatorial Enumeration. That whole class was a rollercoaster ride of mind-blowing generating functions to prove crazy things. The exam had ridiculous questions like 'count the number of cactus trees with n vertices such that etc etc etc' and you'd do three pages of terrible terrible sums and algebra. Then your final answer would be something beautiful like n/2 and you'd breath a sigh of relief and thank the math gods.
8x - 7 = 3x + 9
8x - 3x = 9 + 7
5x = 16
x = 16/5 = 3 1/5
Answer:
The maximum revenue is 16000 dollars (at p = 40)
Step-by-step explanation:
One way to find the maximum value is derivatives. The first derivative is used to find where the slope of function will be zero.
Given function is:

Taking derivative wrt p

Now putting R'(p) = 0

As p is is positive and the second derivative is -20, the function will have maximum value at p = 40
Putting p=40 in function

The maximum revenue is 16000 dollars (at p = 40)
I’m pretty sure you add 78+55= 133
180-133=47
so 9x+2=47
subtract 2 from 47 and itself
so 9x=45
divide 9 and 45 by 9
so x=5