Question

An electronics company has developed a new hand-held device. The company predicts that the start-up cost to manufacture the new product will be $225,000, and the cost to make one device will be $7.50. If the company plans on selling the devices at a price of $9, write and solve an inequality to determine how many must be sold for the company to make a profit. Show your work.

Answer 1

So we'll do this in pieces.
what is the cost of the company?
cost of company to start = ?

Answer 2

225,000

Answer 3

yes, so
profit = -22500
now if we we want to make any money, profit, we need to sell devices, what would the eqwuation look like if I wanted to know how much money I make for each device I sell?

Answer 4

umm im not sure

Answer 5

it would look like this:
how much money is made when each device is sold=9*x
where x is the number of devices sold

Answer 6

I have to go soon..

Answer 7

ok

Answer 8

so now our equation would look like this:
profit = 9*x -22500
can you do what I did with the 9x but with how much it costs to make each device?

Answer 9

yes
7.50*x-22500 right?

Answer 10

very good, but I was a bit confusing when I asked you to do it ^_^
so now if we combine all the parts, the
-22500 and
9*x and
-7.50*x
we get
profit = 9x-7.5x-2500

Answer 11

ok

Answer 12

profit = 9x-7.5x-22500
now we need to set the equation equal to x
so we move the 22500 to the other side:
22500 = 9x-7.5x
now we factor out the x on the right side
22500 = x(9-7.5)
simpilfy
22500 = x(1.5)
divide both sides by 1.5
22500/1.5 = x
now change the = sign to an inequality
22500/1.5 < x
so in order for a company to make any profit, x must be greater than 22500/1.5

so, I sorta rushed it all at the end, but I have to go ^_^

Answer 13

alright, thank you for the help!!

Answer 14

^_^ we did the hard part of setting up the equation. and all the stuff I rushed was just algebra stuff