Step-by-step explanation:
If x is the number of t-shirts, and y is the number of sweatshirts:
10x + 15y ≥ 500
x + y ≤ 50
y ≥ x/2
And since x and y can't be negative:
x ≥ 0
y ≥ 0
Graph:
desmos.com/calculator/mw6dsei6jm
The boundaries of the feasible region are:
(0, 50), (0, 33.3), (28.6, 14.3), and (33.3, 16.7)
Since x and y must be integers, any non-integer solutions are not viable.
The maximum profit will be when the most product is sold. Since sweatshirts are more profitable, we want to sell as much of that as we can.
So they should sell 0 t-shirts and 50 sweatshirts for a maximum profit of $750.
