Find the System of Equations to Model the Problem

question 4

Essay

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
-In producing three types of bricks: face bricks, common bricks, and refractory bricks, a factory incurs labor,
material, and utility costs. To produce one pallet of face bricks, the labor, material, and utility costs are $50, $75,
and $35, respectively. To produce one pallet of common bricks, the labor, material, and utility costs are $50, $60,
and $30, respectively, while the corresponding costs for refractory bricks are $75, $100, and $45. In a certain
month the company has allocated $12,000 for labor costs, $14,500 for material costs and $6,000 for utility costs.
How many pallets of each type of brick should be produced in that month to exactly utilize these allocations?
Set up a system of linear equations, letting x, y, and z be the number of pallets of face, common, and refractory
bricks, respectively, that must be produced in that month.

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Definitions:

Population Slope

The slope of the regression line that represents the relationship between two variables across the entire population.

Linear Relationship

A type of relationship between two variables where a change in one variable is associated with a proportional change in the other variable.

API Gravity

A measure of the density of petroleum liquids relative to water, used in the petroleum industry to classify oils.

Coefficient Of Correlation

A quantitative analysis that measures the potency and vector of a linear correlation between two entities.