Calculating Profit for DVD Manufacturing with Linear Relationship

[stanton]

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?

 

[berkeman]

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.

 

[stanton]

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.