Find A Math Model

mathdad

mathdad

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Apr 24, 2015
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The price p (in dollars) and the quantity x sold of a certain product obey the demand equation x = -5p + 100, where 0 < p less than or equal to 20. Find a model that represents the revenue R as a function of x. Note: Revenue = price x quantity sold or in short R = px.

Let me see.

R = px

Solve x = -5p + 100 for p.

x - 100 = -5p

(x - 100)/-5 = p

-(x/5) + 20 = p

Plug into R = px.

R = [-(x/5) + 20]x

R = -(x^2)/5 + 20x

Correct?
 
Last edited:
Part of what my signature means is that you don't have to be married to the vague, and all-too-common concept that you must solve by isolating your target on any particular side. Try doing things that make your life easier. You do seem not to like dividing be negative numbers. Maybe just don't do that at all.

x = -5p + 100

x + 5p = 100

5p = 100 - x

p = (100 - x)/5

Fewer negatives. Fewer parentheses. Less confusion. Less chance of error.

"=" is reflexive.
 
tkhunny said:
Part of what my signature means is that you don't have to be married to the vague, and all-too-common concept that you must solve by isolating your target on any particular side. Try doing things that make your life easier. You do seem not to like dividing be negative numbers. Maybe just don't do that at all.

x = -5p + 100

x + 5p = 100

5p = 100 - x

p = (100 - x)/5

Fewer negatives. Fewer parentheses. Less confusion. Less chance of error.

"=" is reflexive.
Click to expand...

Can we write p = (100 - x)/5 as (1/5)(100 - x) if needed?
 
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