Maximizing profit.. CANNOT get this! please help!

[ErieLees]

the question is:

A CD company has been selling 1200 computer game CDs per week at $18 each. Data indicates that for each $1 price increase, there will be a loss of 40 sales per week. If it costs $10 to produce each CD, what should the selling price be in order to maximize the profit?
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NOW, what I do know is that you have to have a "let X =" statement at the beginning of the solution, and i know that it involves the formula
profit = revenue - cost..
my math teacher always makes us set up a chart showing the initial situation and then the new situation. i just dont really understand how to get the actuall equations to plug into the profit = revenue - cost thing.. can anyone see a solution to this???

 

[galactus]

Let x = the number of $1 increases.

The revenue is then given by:

\(\displaystyle \L\\R(x)=(1200-40x)(18+x)\)

 

[stapel]

A CD company has been selling 1200 computer game CDs per week at $18 each. Data indicates that for each $1 price increase, there will be a loss of 40 sales per week. If it costs $10 to produce each CD, what should the selling price be in order to maximize the profit?

Work with known (and small) numbers, until you see a pattern:

. . .original case:
. . . . .price per: 18
. . . . .sold: 1200
. . . . .income: (18)(1200)

. . .1 increase:
. . . . .price per: 18 + 1(1)
. . . . .sold: 1200 - 1(40)
. . . . .income: (18 + 1)(1200 - 40)

. . .2 increases:
. . . . .price per: 18 + 2(1)
. . . . .sold: 1200 - 2(40)
. . . . .income: (18 + 2)(1200 - 80)

...and so forth, until you can see what "x" ought to stand for, and where it would fit in a formula for "income". :wink:

Eliz.