population gathers plants and animals for survival. They need at least 440 units

Question

population gathers plants and animals for survival. They need at least 440 units of energy, 300 units of protein, and plants provides 30 units of energy, 10 units of protein, and O hides. One animal provides 20 units of energy, 25 units of protein, and 1 hide. Only26 units of plants and 29 animals are available. It costs 20 hours of labor to ours for an animal. Find how many units of plants and animals should be gathered to meet the requirements with a minimum number of hours of labor The population should gather (Simplify your answers.) animals. 22 units of plants and

Explanation / Answer

Let x = number of units of plants and y = number of units of animals. Then, the given conditions translate into the following LPP (Linear Programming Problem).

Minimize Z = 20x + 12y subject to

30x + 20y 440

10x + 25y 300

              y 8

x, y 0.

Solving the above LPP graphically, the optimum solution is found to be: x = 0 and y = 22 and the corresponding minimum cost is 264. Thus, the answer is:

The population should gather 0 units of plants and 22 units of animals. ANSWER

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