Calc student stuck on business application: revenue for 1 additional item

In summary, the question is asking for the additional revenue made by selling an extra 1 ton of ore on top of the amount needed to maximize profit. This can be calculated by subtracting the revenue at the maximized amount from the revenue at the maximized amount plus 1 ton of ore. However, the question is poorly worded and could be interpreted in different ways.
  • #1
Lebombo
144
0

Homework Statement



A company mines low-grade nickel ore. If the company mines x tons of ore, it can sell the ore for the price p = 225 - 0.25x dollers per ton.

How much revenue will the company make by selling an additional 1 ton of ore on top of what is being produced to maximize revenue.

Homework Equations

I made revenue be: R(x) = 225x - 0.25x[itex]^{2}[/itex]

Critical point: [R'(x) = 0] --> [225 - .5x = 0] --> [x = 450]

Setting up a table shows x = 450 is a max value.

The Attempt at a Solution

Now here is where I get stuck. I don't know what the question is asking me to find.Guess 1) Is the question asking for the total revenue realized by the company at the 451st item? If so, I would probably just evaluate f(451) = 50,624.75

Guess 2) Is the question asking for the revenue of the 451st item by itself? If so, I would probably then evaluate f(451) - f(450) = -225.25 (negative revenue)

Guess 3) Or the approximate revenue of the 451st item? Which I assume would be evaluated using the derivative R'(450) = 0Any of these 3 calculations match what the question is asking for?
 
Last edited:
Physics news on Phys.org
  • #2
Yes the question is poorly worded, my guess would be that you are asked to find the revenue made by producing the amount of ore required to maximize profit, and then add to that the revenue from 1 more ton of ore.
 
  • #3
any help out there on the interwebs?
 
  • #4
Oops Poopsilon, didn't realize I had a reply already. Thanks.

So if it is the case that you say, wouldn't adding the exact revenue from one additional ton (451st ton) to the total revenue up to 450 tons be the same value as f(451)?

In other words, [f(451) - f(450)]+f(450) = f(451)

I'll ask my professor what he meant exactly. Thanks for your help.
 
  • #5
Sounds like they are looking for R(n+1) - R(n). With that information, you could generalize something like, "We can make x dollars selling n things, and we make x+y dollars selling n+1 things. The ratio of y/1 might be really small in comparison to the ratio of x/n. That is, it might not be worth producing anything over the maximized amount.

But that is a horrible question. They might just want R(n+1).
 

What is the formula for calculating revenue for 1 additional item?

The formula for calculating revenue for 1 additional item is (Price of Item x Number of Additional Items Sold) - (Fixed Costs + Variable Costs)

How is revenue affected by increasing the price of an item?

Increasing the price of an item will lead to an increase in revenue if the demand for the item remains constant. However, if the demand decreases due to the price increase, the revenue may also decrease.

What factors affect the fixed costs in a business application?

The fixed costs in a business application can be affected by factors such as rent, insurance, salaries, and utilities. These costs remain constant regardless of the number of items sold.

What are some examples of variable costs in a business application?

Some examples of variable costs in a business application include the cost of materials, shipping, and commissions. These costs can change based on the number of items sold.

How can a business increase its revenue without increasing the price of its products?

A business can increase its revenue by increasing the number of items sold, improving the efficiency of its production process, or finding ways to reduce variable costs. Additionally, implementing marketing strategies to attract more customers can also help increase revenue.

Hot Threads

Recent Insights

Back
Top