SOLUTION: You are selling banana bread that costs P 5 each. Each week, you have 50 customers. When you decrease the price by P1, you expect 30 customers to be added. What is the price of t

Algebra ->  Functions -> SOLUTION: You are selling banana bread that costs P 5 each. Each week, you have 50 customers. When you decrease the price by P1, you expect 30 customers to be added. What is the price of t      Log On


   

Question 1064483: You are selling banana bread that costs P 5 each. Each week, you have 50
customers. When you decrease the price by P1, you expect 30 customers to be
added. What is the price of the banana bread that yields a maximum profit?
c. If the revenue (R) = number of customers × bread price. Write the
equation of the quadratic function given the situation above?

how did you get the letter c in question 916733?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You are selling banana bread that costs P 5 each. Each week, you have 50
customers. When you decrease the price by P1, you expect 30 customers to be
added. What is the price of the banana bread that yields a maximum profit?
c. If the revenue (R) = number of bread × bread price. Write the equation of
the quadratic function given the situation above?
Let x = the number of p30 reductions in price 

Then

the price will be reduced from p(5) to p(5-1*x), or p(5-x)

and

the number of customers will grow from 50 to 50+30x

Profit = (50+30x)(5-x)
Profit = 250-50x+150x-30x2
Profit = 250+100x-30x2
Profit = -30x2+100x+250

Maximum profit, use vertex formula x=-b%2F%282a%29=-100%2F%28%282%29%28-30%29%29=100%2F60+=+%221.666...%22

So we reduce the price by 1.666... reductions of 1p each.

So the new reduced price is p5 to p5-p1.666... = p3.333...

Edwin