How many units of each type should be sold in order to maximize total profit?

A store sells two types of sodas, A and B. The store owner pays $8 and $10 for each one unit of soda A and B respectively. One unit of sodas A yields a profit of $2 while a unit of sodas B yields a profit of $3. The store owner estimates that no more than 2000 sodas will be sold every month and he does not plan to invest more than $20,000 in inventory of these sodas.
How many units of each type of toys should be stocked in order to maximize his monthly total profit?

1 Answer
May 7, 2018

The store owner should buy 2000 units of soda B and 0 units of soda A.

Explanation:

The soda which yields the greatest profit is soda B, so the owner must try to stock the most of that. The first restriction we will evaluate is the total price of #$20,000#. Each unit of soda B costs #$10#, so the owner can buy up to #2000# units of soda B per month (#$10x=$20,000->x=2000#). The next restriction is the units to be sold. The owner estimates a maximum sale of #2000# units. Therefore, since he can buy up to #2000# units of soda B, he should!