lowest and highest price

Question

The demand equation for a certain product is given by p=112−0.085x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R=xp.

Answer 1

I'm not 100% sure I understand your question, but I have some information that might help you.

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Max price you can sell for :

Set x = 1 (cannot be 0, since then you wouldn't be selling anything)

p_max = 112-.085*(1) = $111.915 ~ $111.92

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Min price will eventually be $0 at a certain number of units produced

0 = 112 - .085x

Add .085x to both sides

.085x = 112

divide both sides by .085

x ~ 1317.65

the 1318th unit would be "free"

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Max Revenue

R = x*p = x*( 112 - .085x ) = 112x - .085x²

Since the 'x²' part of the equation has a negative coefficient, the parabola has a Max at (-b / 2a), which is the center of a parabola

b = 112

a = -.085

solve for : -b / 2a (center of a parabola)

-112 / ( 2*( -.085 ) ) = 658.824 ~659th produced unit (can't produce partial units)

So you maximize revenue if you produce only 659 units at a time.

R_max = x*p = 359* (112 - .085*359) = $36,894.115

R_max ~ $36,894.12

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So above, I solved the 3 points of the parabolic Revenue curve

Point 1 (just above a root) : Production = 1, Price = $111.92, Revenue = $111.92

Point 2 (max of the curve) : Production = 659, Price ~ $55.99, Revenue ~ $36894.12

Point 3 (a root) : Production = 1318, Price ~$0, Revenue ~$0

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Again, not sure if this was what you were asking, but here is something