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- anonymous

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

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- anonymous

- katieb

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- anonymous

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.

- dumbcow

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

- dumbcow

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

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