Answer: 20
<u>Step-by-step explanation:</u>
- Step 1: Find the vertices (intersections) of the constraints by either graphing or solving the system of equations. I graphed them and found two of the vertices: (0, 1) and (4,0) but needed to solve the system to find the third vertex (point of intersection).
-x + 3 = + 1
<u>+x -1 </u> <u> +x -1 </u>
2 =
(3)2 =
6 = 4x
<u> ÷4 </u> <u>÷4 </u>
= x
y = + 1
= + 1
= + 1
=
Third vertex is at
- Step 2: Input the vertices into the objective function: C = 5x - 4y
(0, 1): C = 5(0) - 4(1)
= 0 - 4
= -4
: C = 5
- 4
= -
=
= 1.5
(4, 0): C = 5(4) - 4(0)
= 20 - 0
= 20
- Step 3: Evaluate the answers above to find the maximum: <em>20</em>