Thread: Maximum profit question

it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
n=a/x-10+b(100-x),
where a and b are positive constants.what selling price will bring a maximum profit?

What have you tried here?

To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.

Originally Posted by university

it costs you 10 euros per backpack to manufacture and distribute backpacks.if the backpacks sell at x euros each (where 15=or< x=or<100) the number sold is given by
n=a/x-10+b(100-x),
where a and b are positive constants.what selling price will bring a maximum profit?

Profit = price*number sold - cost of production

In this case is the cost of producing one unit so the cost of produceing units is , so you end up with and the profit on one unit is :

Profit=

Now when you simplify the right hand side of the above you will end up with a quadratic expression in , and you have to find the maximum of this subject to the constraints on x.

(the last part can be done without calculus by completing the square)

CB

Originally Posted by pickslides

What have you tried here?

To find a maximum with these types of problems often require you finding a derivative and solving for the zeros.

This is a problem in finding the maximum of a quadratic, no calculus required.

CB