B&K is a grocery store selling two soft drink types: A$1$ and B$1.$ The profit margin on the first drink is $$5/$can$,$ while on the

second is $$7/$can$.$ B&K does not sell more than $500$ cans per day. Although A$1$ is the best$-$known brand, customers tend

to buy more of the B$1$ brand because it is cheaper. Therefore, it is estimated that sales of the B$1$ brand outperform A$1$ by

at least a $2$:$1$ ratio. Finally, the store sells at least $100$ cans of A$1$ per day

The answer should be:

$100$ cans of A$1$ and $400$ cans of B$1$ should be sold to maximize profit. And the profit would be $$3300$

$1.$ Write the equations of the optimization model: decision variables, objective function, and constraints.

$2.$ Find the optimal solution through the graphical method

$3.$ What is the optimal solution?