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## Homework Statement

cellphones are sold at price of 302$ per unit

In one week there were 450 units sold.

for every one dollar increase in unit price, the weekly sales of the phones fell by four units.

form a function which describes the weekly sales income when the phone's price changes by X dollars

Can the store sell cellphones at the price of 522 dollars?

## Homework Equations

3. The Attempt at a Solution [/B]

I know that sales = turnover. But it does not seem to be the way to properly calculate this problem.

I had the wrong function evidently as my teacher sent me the correct solution to this problem. But I wonder if my original way is sensible or not.

I wonder if I should have somehow created a function which describes the weekly sales, from a zero units sold beginning. Like at the beginning hours of the business week, obviously nothing has been sold at that beginning hour. Past weekly sales would not matter in this sense, because new weekly sale is being calculated.

Normally of course turnover is the units sold times the price/unit.

Immediately it looks like at some point. The unit sale amount will become negative, when the price increases too high. Worst case for store is that nothing is sold = 0 unit sale amount.

302 with no price change would equal 450 units

302+1 would make the change sales to 450 -4

304 would make sales to 450 - 4*2

turnover = y

y = (price/ unit) x (unit amount sold)

y = ( 302 + x) * (450- 4x)

Can the store sell phones, at the unit price of 522?

522- 302 = 220

(302+220) * (450-4*220) = y

522 * ( 450 - 880) = y

522 * - 430 = y

-224460 = y

looks like nothing will be sold at that price,

This looks like it will be the case when one looks at the right hand side inside the brackets ( 450 - 4*220). This number should have been a positive number, for any amount of unit sales to have occured.