How many Cantaloupes and Watermelons should I sell? So I want to sell cantaloupes and watermelons at a farmers market from July - Sept. and I want to make at least $450$.
If I want to sell the cantaloupes for $5.50$ each and the watermelons for $6.75$ each, how many of each should I sell in order to reach my goal?
My problem is trying to solve this equation:
$5.50C+6.75W≥450$ 
[Cont.] the main reason being that I don't know when to flip the 'greater than or equal to' sign. 

Could someone explain how to do the equation with a simple example and then leave it to me to solve it out? 
Thanks for your help! 
 A: For each number of cantaloupes from $0$ to $C_{min}$, where $C_{min}$ is the smallest number cantaloupes such that $5.5 \cdot C_{min} \geq 450$, you can calculate the value of $W(C)$, the minimum number of watermelons that's required to earn at least $450$ for a particular number of cantaloupes.
(Another interpretation of $C_{min}$ is the minimum number of cantaloupes you have to sell to reach your goal, if you sell only cantaloupes.  It's the same equation you have, but with $W=0$.)
For example, $W(10)$ can be found like this:
$$5.5(10) + 6.75W = 450 \to W \approx 58.5,$$
which means $W(10) = 59$.  This is the number of watermelons you have to sell to meet your goal, if you also sell $10$ cantaloupes.
Then, those are your solutions, as well as any number of watermelons larger than $W(C)$.  (If you sell $10$ cantaloupes, you can call $59$ watermelons, or $60$, or $357$, and also meet your goal.)  Also, of course, any number of cantaloupes greater than $C_{min}$, and any number of watermelons will also work.
