Here are the constraints
y ≥ x + 100
x + 2y ≤ 1400
And we seek to maximize this
14x + 22y - 900
Here's the graph of the constraints : https://www.desmos.com/calculator/rjxwpnzj24
a. We have only one vertex at (400,500)
b. This point is a corner point.....the profit max occurs here
So....the max profit is 14(400) + 22(500) - 900 = $ 15700