Word problem

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karliekay

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The demand for a certain product described by D(p)= -0.02p^2+1000, 0=<p=<400, where p is the selling price in dollars. The selling price p is given by p(c)=4c-20, c=< 20, where c is the production cost of the product. Find D(c), the demand function in terms of the production cost.

Ok I got -.32c^2+3.2c+992. The part I dont know is I need to put where the cost (c) goes from. like 0=<c=< 400.
 
karliekay said:
The selling price p is given by p(c) = 4c - 20, c =< 20, where c is the production cost of the product.

I do not understand how a production cost can be negative. Are you sure that you typed the proper domain for p(c) ?
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karliekay said:
production cost is not negative it is P(c) = 4c-20 Huh ?

You first wrote that p is the selling price and c is the production cost.

I'm more confused now, not less.
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karliekay said:
The way the orginal problem is written is the way it is written in the book.

This statement makes your last post false.

You confuse me, when you post false information.
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Your original post states, "c is the production cost".

That post also states, "c =< 20".

I do not understand how a production cost takes on negative values.

Since you've double-checked, and c =<20 is what you were given, I'm now thinking that something is wrong with the given information; somebody else will have to help you.

 
You're almost done. You already have an upper limit for c (20, given). If you substitute 4c-20 for p in the range given for p, you'll get the lower limit.
 


I thought c<=20 was a domain statement, since it directly follows the function definition. :roll:

I'm trying to point out that the numbers in this exercise do not jive.

Let's say that the production cost is at your so-called maximum: $20. Then the maximum selling price is $60. But, you've stated that the selling price ranges from $0 (whatever that's supposed to mean) all the way through $400.

Do you understand? p will never be more than 60, if c is limited to 20.

If $400 is a correct figure for the maximum p, then 5 <= c <= 105; otherwise, who knows what's going on ?

c = 5 comes from solving for p = 4c - 20, using the smallest number in the given range of selling prices: $0. Ridiculous.

 
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