How do you find maximum revenue, maximum profit, and minimum average cost? Our teacher gave us a project to teach ourselves the section, but I can't learn very well even with her teaching, so I don't know how I'm supposed to do this...
revenue is price * quantity
profit is revenue - cost
avg cost is totalcost/quantity
as usual, max/min is found via the derivative
I don't remember how to did min/max. I can get as far as the critical numbers...
if you can find the critical numbers, that is where the derivative is zero. That is the point of min/max of the function.
Check some of the related links below; you will find such problems worked out.
Also, a net search for minimum revenue and such will produce many examples showing the method.
Finding the maximum revenue, maximum profit, and minimum average cost involves different principles and techniques. I'll try to explain each one to help you understand how to approach these problems.
1. Maximum Revenue:
Maximum revenue refers to the highest amount of income generated by a business within a given period. To find the maximum revenue, you need to understand the revenue function and its relationship with the input variables.
a) Revenue Function:
Start by identifying the revenue function specific to your project. For example, if your project involves selling a product, the revenue function could be calculated by multiplying the price of the product by the quantity sold.
b) Optimization:
To find the maximum revenue, you need to optimize the revenue function with respect to the input variables. This typically involves finding the critical points of the revenue function by taking the derivative, setting it equal to zero, and solving for the input variables.
2. Maximum Profit:
Maximum profit represents the highest amount of financial gain a business can achieve. It involves understanding the relationship between revenue, costs, and profit.
a) Cost Function:
Identify the cost function relevant to your project. For example, if you're selling a product, the cost function could include factors such as production costs, advertising costs, and any other costs associated with your business.
b) Profit Function:
The profit function is calculated by subtracting the cost function from the revenue function. In mathematical terms, Profit = Revenue - Cost.
c) Optimization:
To find the maximum profit, you need to optimize the profit function similarly to maximizing revenue. Take the derivative of the profit function, set it equal to zero, and solve for the input variables.
3. Minimum Average Cost:
The concept of average cost refers to the cost per unit of production. Minimizing the average cost involves finding the most cost-efficient way to produce a given quantity of output.
a) Total Cost Function:
Start by identifying the total cost function specific to your project. It represents the overall cost of production given the quantity produced.
b) Average Cost Function:
The average cost function is calculated by dividing the total cost by the quantity produced. In mathematical terms, Average Cost = Total Cost / Quantity.
c) Optimization:
To find the minimum average cost, optimize the average cost function by taking its derivative, setting it equal to zero, and solving for the input variables.
Remember, these explanations provide a general understanding of the concepts, but the specifics may vary based on your project requirements. Additionally, if you encounter any difficulties, it's always a good idea to seek assistance from your teacher or classmates.