Question 747923: A Grocery store sells 4000 bags ( 4 litres each) of milk per week when the price is $5.50 for a bag. Customer research indicates that for each $0.10 decrease in the price, 200 more bags of milk will be sold. The store wants to bring in $27,500 for the bags. What price should the grocery store charge?
a) Set up the solution with let statements and an algebraic expression.
b) Use the quadratic formula to determine the roots of the equation.
c) How many price decreases would be required for the store to bring in $30,000?
d) What would the price need to be for the bag of milk and how many bags would be sold at the store?
Please help me. My dad ( who works as a Soils Engineer) and I have tried for four hours and haven't gotten an answer that actually works. Please help me
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! Let N equal the number of 10 cent price drops.
Bags that will be sold = 4000+200N
New price per bag = 5.50-.1N
Revenue = (4000+200N)(5.5-.1N)
R = 22000+1100N-400N-20N^2
R = -20N^2+700N+22000
This is a downward facing parabola. We aren't interested in the zeros, but in the maximum as we wish to maximize dollars.
The vertex is at -b/2a = -700/(2*-20) = 17.5
The equation doesn't care that it started with a dime change to move sales. The maximum revenue is at 5.50 - 1.75 = $3.75 and 4000+200(17.5) = 7500 bags sold, for max revenue 7500*3.75 = $28125
I solved max revenue, you can't get over $30,000. Set R=$27,500 and solve if you'd like.
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