It moves roughly 5 inches a day. (p.s you made a mistake, there is 365 days in a year not 356)
Solution: (3x + 4y - 3z) x (3x + 4y + 3z)
You can't make a triangle with those lengths for sides.
The way I look at it is like this:
-- Take 2 sticks ... lengths 4 and 2 ... and connect them together at one end.
-- The farthest they can reach, if they're opened up completely and pointing
in opposite directions, is a distance of 6 .
-- They can't reach the ends of a stick that is 7 long. So you can't make
a triangle with those 3 sticks.
a. R\p = (10 - q)*2
The inverse demand function is just the inverse function of the demand function. In other words, we just have to isolate p in the demand function:
p = (10 - q)*2
b. R\25
The price for 5 units of output is given by the inverse demand function:
p = (10 - 5)*2 = 10
We replace p in the profit function:
π(q) = 10 * 5 - 5² = 25
c. 3
For this one, we replace the inverse demand function in the profit function and derivate for q, then equate to 0 and solve:
π(q) = ((10 - q)*2)*q - q² = 20q - 2q² - q² = 20q - 3q²
dπ/dq = 20 - 6*q
20 - 6q = 0
q = 20/6 = 3.33333
Now, a decimal level of output makes no sense. So, now we try the nearest integers 3 and 4, and find the respectives profits. The output that has that maximum profit will be the one that maximizes the profit. Keep in mind, that this will only be true in this particular case because the profit function has the form of a quadratic equation:
π(3) = 20 * 3 - 3*(3)² = 33
π(4) = 20 * 4 - 3*(4)² = 32
The answer is 3.
