Find the marginal profit function given a function for demand and cost

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Homework Help Overview

The problem involves determining the marginal profit function for a nursery based on a given demand function for potted plants and a cost function. The demand is expressed as a price function, while the cost function outlines the expenses associated with growing a certain number of plants.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between price, demand, and profit, with some questioning how to derive profit without a clear selling price. Others suggest that the demand function indicates price based on quantity sold.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the demand function and its implications for calculating revenue and profit. Some guidance has been offered regarding the relationship between revenue and cost, but no consensus has been reached on the interpretation of the demand function.

Contextual Notes

There is uncertainty regarding the interpretation of the demand function and its role in determining profit, as well as the absence of explicit selling price information. Participants are also navigating the constraints of the problem as presented.

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Homework Statement


A nursery has determined that the demand in June for potted plants is p= 2.00 - (x/30000). The cost of growing x plants is C = 2000 + .20x, 0 \leq x \leq 100000
Find the marginal profit function.

Homework Equations


N/A


The Attempt at a Solution


I don't know where to begin, mostly because I don't see any way of determining profits because it never gives you any indication of what price they are selling them for, only the costs, is there something I'm missing or is this problem simply unsolvable?
 
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Runaway said:
A nursery has determined that the demand in June for potted plants is p= 2.00 - (x/30000). The cost of growing x plants is C = 2000 + .20x, 0 \leq x \leq 100000
Find the marginal profit function.

Cost = 2000 + .20x

Revenue = Price*Quantity (where demand indicates price)
Revenue = ...?

Once you have revenue and cost, what's the equation for profit? Once you have profit, how do you get marginal profit?
 
I think you are miswriting the "demand". I think that "p" is the price and "x" is the number sold. That is, solving the equation for x, the demand is given by x= 3000(p- 2.00), where p is the price.
 
demand is what it says in the problem, that's what I didn't understand
 

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