Ahhh Applied Calc problem, i need an answer by 2am, thats when it is due HELP

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Homework Help Overview

The discussion revolves around an applied calculus problem involving profit maximization based on a given cost function and selling price. Participants are tasked with determining the maximum profit from producing and selling goods, with specific emphasis on the relationship between marginal cost and selling price.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting up the profit function by subtracting costs from income and consider taking derivatives to find maximum profit. There is mention of the marginal cost and its relationship to profit maximization, with some questioning the utility of analyzing marginal cost separately.

Discussion Status

The discussion is active, with various approaches being explored. Some participants suggest deriving the profit function and finding its maximum, while others highlight the importance of equating marginal cost to selling price. There is no explicit consensus, but multiple interpretations and methods are being considered.

Contextual Notes

Participants are working under a time constraint, as the problem is due soon. The original poster expresses urgency in finding a solution, which may influence the direction of the discussion.

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Ahhh! Applied Calc problem, i need an answer by 2am, that's when it is due! HELP!

the cost of producing q goods = .4q^2 + 10q

the marginal cost is given by the derivative, .8q + 10

what is the maximum profit if each item is sold for 19 dollars (assume you sell everything you produce)
 
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set up the profit function (income minus costs) and then take the derivative of the whole thing and set it equal to zero. looking at marginal cost separately is not that useful (though, of course, by taking the derivative of the whole thing and setting it equal to zero you'll be looking for that magic point where the marginal cost and marginal profit are equal)
 
profit=price of producing q goods-cost of producing q goods =>

profit= 19(q)-(.4q^2 +10q) =9(q)-.4q^2 from here you need either to find the vertex of this parabola or to derivate for its maximum.
 
Since you are given the marginal cost, the maximum profit occurs when the price of the item equals the marginal cost. (Producing one more would make the cost greater than the price and you start losing money.)

That is .8q+ 10= 19. Solve that for q and then find:
1) income: 19q
2) cost .4q^2 + 10q
3) Subtract to find profit.
 

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