Answer:
(a)
(b)
(c)R'(5400)=$394
Step-by-step explanation:
Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:
p = −0.02x + 610 (0 ≤ x ≤ 20,000)
(a)Revenue function R.
Revenue = Price X Quantity Demanded
Therefore:
R(x)=xp
(b)Marginal revenue function R'(x)
If
Then, the marginal revenue function
(c)We want to compute R'(5,400)
From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.
Answer:
Container will have less label area than container
by about
.
Step-by-step explanation:
A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.
Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of and a radius of
at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width
and length
.
Apply this reasoning to both cylinder and
:
For cylinder ,
while
. Therefore, when the lateral side of this cylinder is unrolled:
That corresponds to a lateral surface area of .
For cylinder ,
while
. Similarly, when the lateral side of this cylinder is unrolled:
That corresponds to a lateral surface area of .
Therefore, the lateral surface area of cylinder is smaller than that of cylinder
by
.