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.

---

Definitions:

Assembly Department

A division within a manufacturing facility where parts are put together to assemble the final product.

Beginning Work

The inventory of production that has not yet been completed at the start of a financial or reporting period.

Process Inventory

The amount of inventory that is currently undergoing manufacturing or production processes.

Conversion Costs

The total cost of converting raw materials into finished goods, including both labor and manufacturing overhead expenses.