# Boxes of Candy

• January 14th 2007, 04:52 AM
symmetry
Boxes of Candy
The monthly revenue achieved by selling x boxes of candy is figured to be
x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. How many boxes must be sold each month to achieve a profit of at least$60?

How many boxes must be sold each month to achieve a profit of at most $60? In terms of inequality word problems, what is the difference between at least and at most questions? Thanks • January 14th 2007, 04:59 AM Quick To say $x$ is at least 50, you would write: $x\geq 50$ To say at most 50 you would write: $x\leq 50$ • January 14th 2007, 05:25 AM symmetry ok Great information given but what are the steps for me to find the answer? Can you set up an equation? • January 14th 2007, 06:08 AM CaptainBlack Quote: Originally Posted by symmetry The monthly revenue achieved by selling x boxes of candy is figured to be x(5 - 0.05x) dollars. The wholesale cost of each box of candy is$1.50. How many boxes must be sold each month to achieve a profit of at least $60? Profit is revenue-costs, so in this case: p=x(5-0.05x) - 1.5x=-0.05 x^2 + 3.5 x we want this to be at least 60 dollars, so we want p>=60. Now as p is a quadratic in x, with a negative coefficient to the x^2 term p>=60 between the roots of: p=-0.05x^2+3.5x =60 or between the roots of 0.05 x^2-3.5 x +60=0. The roots of this quadratic are 30 and 40, so the profit >=$60, for