Calculating Profit for DVD Manufacturing with Linear Relationship

In summary, the manufacturer produces DVD at $2 per unit and sells them at $5 each. With 4000 units sold per month, the manufacturer plans to increase the price by $0.50 and estimates a decrease of 200 units sold per month. The relationship between price and units sold is linear. Using the equations mx+b, the profit can be calculated as -2x^2-8005x-8000 in terms of x, the number of made and sold.
  • #1
stanton
74
0

Homework Statement



A manufacturer produces DVD at $2 per each unit. The selling price is $5 each. 4000 units are soled per month. The manufacturer want to raise the price and estimates that for each $0.50 increases in price, 200 fewer DVDs will be sold each month.
Relationship between DVD price and number sold is linear. Find P(x), the total profit in terms of x, the number of made and sold.

Homework Equations



Equation? mx+b

The Attempt at a Solution



The slope is -2, I think. And I am given point (3, 4000) the reason is that price per unit 5$ minus manufacturing price is 3.
Am I doing right?
 
Physics news on Phys.org
  • #2
stanton said:

Homework Statement



A manufacturer produces DVD at $2 per each unit. The selling price is $5 each. 4000 units are soled per month. The manufacturer want to raise the price and estimates that for each $0.50 increases in price, 200 fewer DVDs will be sold each month.
Relationship between DVD price and number sold is linear. Find P(x), the total profit in terms of x, the number of made and sold.

Homework Equations



Equation? mx+b

The Attempt at a Solution



The slope is -2, I think. And I am given point (3, 4000) the reason is that price per unit 5$ minus manufacturing price is 3.
Am I doing right?

Spend a little more time talking out the problem, before jumping into writing equations (and worse yet guessing at them).

"The profit is the income minus the cost. The cost is the $2 price per unit multiplied by the number of units sold per month. The income is the sell price multiplied by the number of units sold per month. The number of units varies with the sell price."

Now, write an equation for the cost per month versus the volume. And, write an equation for the volume sold per month versus the sell price. Look at these equations a bit, and see if you see a way to combine them, or write a third equation that starts to tie things together.
 
Last edited:
  • #3
Thank you so much for your explanation. I fixed my several datas. So:
we are given point (5, 4000) slope:-2
-2=(5-p)/(4000-x) solve for p: p=8005-2x
total revenue: x(8005-2x)=-2x^2-8005x
profit is -2x^2-8005x-(2)(4000)
So the profit is -2x^2-8005x-8000
For your explanation was simple ans easy to understand, I could figure out the answer quickly. Thank you again.
 

What is a word problem?

A word problem is a mathematical problem that is presented in the form of words or a story. It requires the reader to analyze the given information and use mathematical concepts to find a solution.

How do I approach a word problem?

To solve a word problem, it is important to first understand what the problem is asking for. Then, carefully read the information given and identify any key words or numbers. Next, choose the appropriate mathematical operation(s) and set up an equation to solve for the unknown variable. Finally, check your answer to ensure it makes sense in the context of the problem.

What are some common strategies for solving word problems?

Some common strategies for solving word problems include drawing a picture or diagram, making a table or chart, using a formula or equation, and working backwards from the answer. It is important to choose the strategy that best fits the problem and your personal learning style.

How can I check my work when solving a word problem?

To check your work, you can plug your answer back into the original equation to see if it makes sense. You can also estimate the answer or use a calculator to verify your solution. If possible, try solving the problem using a different strategy to see if you get the same answer.

What can I do if I am still struggling with word problems?

If you are having difficulty with word problems, try breaking the problem down into smaller, more manageable parts. You can also seek help from a teacher, tutor, or classmate. Practicing with a variety of word problems can also improve your problem-solving skills.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
4K
  • General Math
Replies
3
Views
994
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Replies
2
Views
2K
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
25
Views
3K
  • Precalculus Mathematics Homework Help
Replies
4
Views
4K
  • General Math
Replies
2
Views
6K
  • General Math
Replies
1
Views
2K
Back
Top