Answer:
The minimum  labor = 270 hours and it is obtained when 0 units of plants and 18 animals are collected.
Step-by-step explanation:
We assume that x should represent the number of units of plants
Also y to represent the number of animals.
So, minimze (z) = 30 x + 15 y
Subject to:
30 x + 20 y ≥  360 Â
10  x + 25 y ≥ 300
        y  ≤ 8
 0  ≤  x  ≤ 25
 0  ≤  y  ≤ 25
Changing the above linear inequalities into linear equation; we have:
30 x + 20 y = Â 360 Â
10 Â x + 25 y = 300
        y  = 8
The graph for the above discussion can be located in the attached diagrammatic expression below:
NOW, the corner points (0,18),(0,25),(25,25), and (25,8) can be calculated from the graph. From the diagram, the corner point  [tex][\frac{60}{11} , \frac{108}{11} ][/tex] can be found by solving the system.
30 x + 20 y = Â 360 Â
10 Â x + 25 y = 300
Corner point (10, 8) = 10 x + 25 y = 300
                          y  = 8
Corner point                Value of z = 30 x + 15 y
(0,18) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 270
(0,25) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 375
(25,25) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 1125
(25,8) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 870
[tex][\frac{60}{11} , \frac{108}{11} ][/tex]                      [tex]\frac{3420}{11}[/tex] ≅ 310.91
(10, 8) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 420
∴
The minimum  labor = 270 hours and it is obtained when 0 units of plants and 18 animals are collected.
