Minimize and maximize profit

Question

Minimize and maximize p=5x+5y subject to the following constraints:

2x+y≤10

x+2y≤8

x,y≤0

Answer 1

The first step is to graph the constraints and find the vertices. Normally in these problems, the last constraint would be x,y≥0. Is this a typo? I am going to answer the question as is it is greater than.

The vertices are (0,0)(0,4)(4,2)(5,0) You would test each of these is the function.

p=5x+5y

p=5(0)+5(0) = 0 This is the minimum value

p=5(0)+5(4) = 20

p=5(4)+5(2) = 30 This is the maximum value

p=5(5)+5(0) = 25