Question

The unit price of manufacturing a product is P=200-0.01x where x is the number of units produced. assuming all units are sold.
a. what value of production (units) will yield a maximum sales?
b. what is the value of maximum sales?
c. what is the unit price at maximum sales level?

plss. help thank you

Answer 1

If we define x as the number of units produced, we the receive that the total production cost is:
\[xP=200x-0.01x^2\]So, we find the maxima of this curve, one way to do this is differentiation, although your teacher may have taught you a few others:
\[
(xP)'=200-0.02x=0\\
x=10000
\]Which means that, we have minimized the cost per unit at this point. (A)
the value of sales is \[10000P(x)=10000\cdot(200-10000\cdot0.01)=10^6\]Which is our answer to B.
And, as the previous, we simply take
\[
P(x)=200-0.01\cdot10000=100
\]
For C.

Answer 2

sales = price * num of units

sales = P(x) * x

sales = 200x - .01x^2

this is a parabola...to get maximum, find vertex
y = -.01x^2 +200x + 0

x_coord of vertex = -b/2a
where a,b,c are coefficients

x = -200/-.02 = 10,000
plug this in to get y_coord of vertex

Answer 3

@LolWolf way is better...assuming you know calculus

Answer 4

If you don't, you @dumbcow 's way to find the maxima works equally as well.

Answer 5

its for our calculus .. Thank you guys for your help. i get it.. Thak you @LolWolf @dumbcow