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bii17

  • 2 years ago

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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  1. LolWolf
    • 2 years ago
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    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.

  2. dumbcow
    • 2 years ago
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    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

  3. dumbcow
    • 2 years ago
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    @LolWolf way is better...assuming you know calculus

  4. LolWolf
    • 2 years ago
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    If you don't, you @dumbcow 's way to find the maxima works equally as well.

  5. bii17
    • 2 years ago
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    its for our calculus .. Thank you guys for your help. i get it.. Thak you @LolWolf @dumbcow

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