please see this simple linear programming exercise and its solution from my textbook. The task is to convert the prose and matrix to a formal linear programming problem.
My answer matched theirs except I got different constraints:
$2.5x_A + 3x_B + 2x_C + 4x_D + r = 1400$ (This one is OK)
$10x_A + 12x_B + 8x_C + 15x_D + s = 150$ (apparently 150 is incorrect)
$5x_A + 7x_B + 4x_C + 9x_D + t = 80$ (apparently 80 is incorrect)
$x_A + x_B + x_C + x_D + u = 500$ (this is not in the solution at all: I wrote this because they say "market research says they will sell at most 500 each week")
Could someone explain to me where I have gone wrong? Why are 150 and 80 incorrect? Why is my last constraint not actually a constraint?
I have highlighted the areas of confusion in green below. Thanks!