Maximizing profit given cost and demand functions

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In summary, the conversation was about finding the production level that will maximize profit using the cost function C(x) and demand function p(x). The suggested method was to find the revenue function R(x), take its derivative to get the marginal revenue, and set it equal to the derivative of the cost function, which is the marginal cost. The equations were manipulated to get 100,000=900x+x^2, but it is unclear what mathematical function is being maximized and how to proceed from there.
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HHenderson90
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Homework Statement



If
C(x) = 13000 + 600x − 0.6x62 + 0.004x3 is the cost function and
p(x) = 1800 − 6x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Homework Equations



R(x)=xp(x)

The Attempt at a Solution


Because of the hint, How I thought this question should be answered was to find the revenue function and take the derivative of that which is the marginal revenue and then set it equal to the derivative of the cost function which is marginal cost
So,
R(x)=x(1800-6x)
R(x)=1800x-6x^2
R'(x)=1800-12x

C'(x)=600-1.2x+.012x^2
1800-12x=600-1.2x+.012x^2
1200=10.8x+.012x^2
1200=.012x(900+x)
100,000=x(900+x)
100,000=900x+x^2

is this right? Where do I go from here, can I solve for x at this point? If so how?
 
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what mathematical function are you trying to maximize?
 

Related to Maximizing profit given cost and demand functions

1. What is the concept of "maximizing profit" in terms of cost and demand functions?

Maximizing profit refers to the process of finding the optimal level of production or pricing that will result in the highest possible profit for a company. This is done by carefully analyzing the cost and demand functions, which represent the relationship between the cost of producing a good or service and the demand for it.

2. How do cost and demand functions affect profit maximization?

The cost function represents the expenses incurred in producing a good or service, while the demand function represents the quantity of that good or service that consumers are willing to buy at a given price. By understanding these functions and their relationship, a company can determine the optimal level of production or pricing that will result in the maximum profit.

3. What factors should be considered when maximizing profit using cost and demand functions?

When maximizing profit, it is important to consider not only the cost and demand functions, but also external factors such as market trends, competition, and consumer behavior. A company must also take into account any fixed costs, variable costs, and pricing strategies in order to make informed decisions.

4. Can a company continue to maximize profit indefinitely using cost and demand functions?

The concept of profit maximization using cost and demand functions is based on the assumption that all other factors remain constant. However, in reality, market conditions and consumer preferences are constantly changing, which may affect the cost and demand functions. Therefore, a company may need to regularly reevaluate and adjust its strategies in order to continue maximizing profit.

5. Are there any limitations to using cost and demand functions for profit maximization?

While cost and demand functions are useful tools for determining profit maximizing strategies, they do have some limitations. These functions are based on assumptions and may not accurately reflect real-world situations. Additionally, they do not take into account external factors such as government regulations or unforeseen events, which may impact a company's profit. Therefore, it is important to use cost and demand functions in conjunction with other tools and strategies when making business decisions.

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