A Company Manufactures a Product Using X, Y and Z $Q = 60 x ^ { \frac { 1 } { 3 } } y ^ { \frac { 1 } { 4 } } z ^ { \frac { 2 } { 5 } }$

question 34

Essay

A company manufactures a product using x, y and z units of three different raw materials.The quantity produced is given by the function $Q = 60 x ^ { \frac { 1 } { 3 } } y ^ { \frac { 1 } { 4 } } z ^ { \frac { 2 } { 5 } }$ .Suppose the cost of the materials per unit is $20, $25 and $75 respectively.
Find the maximum production if the budget is limited to $6000.

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Definitions:

Principle Of Closure

A Gestalt psychology principle stating that individuals tend to perceive incomplete figures as complete by filling in the gaps.

Perceived As Whole

Perceived as whole refers to the psychological phenomenon where an individual or observer views a unit or system as a single, integrated entity, rather than focusing on its individual components.

Perceptual Constancy

The ability of the brain to maintain a stable perception of an object even as sensory input about the object changes (e.g., changes in lighting, angle, or distance).

Retinal Disparity

The slight difference in the visual images that reach each of the eyes, leading to the perception of depth and the ability to see the world in three dimensions.