i cant find anyone who understands this problem!! how did you get this answer!?

Question

The Big Brick Bakery sells more bagels when it reduces its prices, but then its profit changes. The function y = -1000 (x - 0.55) squared + 300 models the bakery's daily profit in dollars from selling bagels, where x is the price of a bagel in dollars. The bakery wants to maximize the profit.


oooyee .. now my question is what would the daily profit for selling bagels for $.40 each && also for $.85 each ..yuck confusion >_<


i cant find anyone who understands this problem!

Answer 1

You obviously didn't ask any people who understand algebra then.

That's a "plug and chug" problem.

if x = 0.40, then the profit would be:

y = -1000(0.4 - 0.55)² + 300 = -1000(.15)² + 300 = -22.5 + 300 = 277.50

You do the other one.

Answer 2

Puggy must have made some error. One need only look at the profit function for a few seconds to see that the maximum profit of 300 is obtained when the price is .55.

Yes, Puggy's mistake is in the second line. The derivative is incorrect. It should be

f'(x) = -2000(x - 0.55)

Setting that equal to 0 yields x = .55.

Answer 3

Since this is a maximize question, this most likely involves derivatives. In order to maximize, you have to take the derivative, make it 0, and solve for the critical points.

y = -1000 (x - 0.55)^2 + 300

y' = -2000 (x - 0.55) + 300
y' = -2000x + 1100 + 300
y' = -2000x + 1400

Now, make y' = 0

0 = -2000x + 1400
2000x = 1400
x = 1400/2000 = 14/20 = 0.70

To get the actual profit, you have to plug in 0.70 for y.

Looks like I didn't answer your question. Oops.

Answer 4

I don't understand the question.