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,

Question

letting x, y, and z be the number of pallets of face, common, and refractory bricks, respectively, that must be produced in that month.

What will be an ideal response?

Answer 1

50x + 50y + 75z = 12,000
75x + 60y + 100z = 14,500
35x + 30y + 45z = 6,000