Question

Suppose that a when a cell phone store charges 16$ for a car charger, it sells 92 units. When it drops the price to 15$ it sells 96 units. Assume that demand is a linear function of price.

If each phone charger costs 1$ to make, what price should the store charge to maximize its profit?
If x is the number of times the price is reduced by one dollar.

Find a function for total profit with respect to x. A negative value for x will mean the price is increased.

Answer 1

well that was wrong. let me try again
if you put the dollar decrease as x, you sell charge
\[16-x\] dollars and sell
\[92+4x\] units for a profit of
\[(16-x)(92+4x)-(2+4x)\] dollars. the last subtraction because your cost is $1 per unit
multiply out and get
\[P=-4 x^2-32 x+1470\]
which will have a maximum at the vertex
\[x=-\frac{b}{2a}=-\frac{-32}{2\times -4}=-4\]

Answer 2

oops wrote again

Answer 3

\[P=(16-x)(92+4x)-(92+4x)=-4 x^2-32 x+1380\]
same vertex though

Answer 4

should increase cost by $4

Answer 5

@turing did we get the same thing? i couldn't tell but maybe i am wrong.

Answer 6

i don't understand why cost is equals (2-4x) can you explain please?

Answer 7

No, your answer makes more sense, I was maximizing Cost to Profit and got a different answer for a different question.

Answer 8

because that was a mistake. you sell
\[92+4x\] units at a cost of $1 per unit, so you have to subtract off your cost. sell
\[92+4x\] units at a price of
\[16-x\] dollars and and at a cost to you of
\[92+4x\] dollars so your total profit, unless i messed up again, is
\[(16-x)(92+4x)-(92+4x)\] representing
the price you charge times the number you sell minus your cost

Answer 9

o nvm...you changed it to (92+4x) that makes so much more sense
thank you guys so much
i was stuck on this question for like half an hour

Answer 10

btw the distributive law tells you taht
\[(16-x)(92+4x)-(92+4x)=(15-x)(92+4x)\] if you want to simplify your calculation before multiplying out