dbporter said:
you wish to sell candy bars and maximize profits. u are able to obtain candy bars at a cost of .20 cents each. from past experience you estimate that if u charge a price of .55 cents u can sell 315 candy bars. u also estimate that each nickel increase in the price will decrease the number of candy bars sold by 15. what should u charge to maximize your profits.
any and all help is appreciated
"u????" Is that supposed to mean "you?"
Standard English is appropriate in any other context than IM-speak or text messages.
That said, how did you try to approach this problem? I would hope you defined a variable, perhaps like this:
Let x = number of 5 cent increases in price
If you increase the price x times 5 cents, the number of candy bars you will sell is
(315 - 15x)
The price you charge for these candy bars will be (55 + 5x)
The amount you receive for selling (315 - 15x) candy bars at (55 + 5x) cents each is
(315 - 15x)(55 + 5x)
Each candy bar costs you 20 cents. So, if you purchase (315 - 15x) candy bars at 20 cents each, your cost will be 20(315 - 15x) cents.
Profit = receipts - cost
Profit = (315 - 15x)(55 + 5x) - 20(315 - 15x)
Note that there is a common factor of (315 - 15x). Remove that common factor:
Profit = (315 - 15x)(55 + 5x - 20)
Profit = (315 - 15x)(35 + 5x)
Profit = 11025 + 1025x - 75x^2
Ok...this is a parabola which opens downward. The maximum profit will occur at the vertex of the parabola. I assume you know how to find that. Remember that we've expressed everything in cents, so when you find the profit, that will be in cents, too....you will probably want to change it to dollars and cents.
I hope this helps you.
