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 2 years ago
The unit price of manufacturing a product is P=2000.01x 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
 2 years ago
The unit price of manufacturing a product is P=2000.01x 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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LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.2If we define x as the number of units produced, we the receive that the total production cost is: \[xP=200x0.01x^2\]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: \[ (xP)'=2000.02x=0\\ x=10000 \]Which means that, we have minimized the cost per unit at this point. (A) the value of sales is \[10000P(x)=10000\cdot(20010000\cdot0.01)=10^6\]Which is our answer to B. And, as the previous, we simply take \[ P(x)=2000.01\cdot10000=100 \] For C.

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0sales = 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
 2 years ago
Best ResponseYou've already chosen the best response.0@LolWolf way is better...assuming you know calculus

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.2If you don't, you @dumbcow 's way to find the maxima works equally as well.

bii17
 2 years ago
Best ResponseYou've already chosen the best response.0its for our calculus .. Thank you guys for your help. i get it.. Thak you @LolWolf @dumbcow
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