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 bread × bread price. Write the equation of
the quadratic function given the situation above?
<pre>
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-30x<sup>2</sup>
Profit = 250+100x-30x<sup>2</sup>
Profit = -30x<sup>2</sup>+100x+250

Maximum profit, use vertex formula {{{x=-b/(2a)=-100/((2)(-30))=100/60 = "1.666..."}}}

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</pre>