Find the Maximum Value of the Objective Function and Where

question 11

Multiple Choice

Find the maximum value of the objective function and where it occurs,subject to the indicated constraints. ​
Objective function:
​
Z = 4x + 5y
​
Constraints:
​
X ≥ 0
​3x - y ≤ 9
2x + 3y ≥ 6
X + 4y ≤ 16
​​ ​

• A)Maximum at (3,0): 12
• B)Maximum at (3,4): 32
• C)Maximum at (4,3): 31
• D)Maximum at (0,4): 20
• E)Maximum at (0,2): 10

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Definitions:

Biological Controls

The use of living organisms, such as predators, parasites, or pathogens, to suppress pest populations and manage ecosystems.

Parasitic Wasps

Insects that play a beneficial role in agriculture by laying their eggs in or on the bodies of other insect pests, eventually killing them.

Ladybugs

Small, dome-shaped insects with distinctive red and black spots, known for their beneficial role in controlling pest populations.

Genetic Engineering

The manipulation of an organism's genes using biotechnology, often involving the transfer of specific traits, or genes, from one organism or species to another to improve or change characteristics.