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A furniture manufacturing company manufactures dining-room tables and chairs. A table requires 12 labor-hours for assembly and 4 labor-hours for finishing. A chair requires 6 labor-hours for assembly and 1 labor-hour for finishing. The maximum labor hours available per day for assembly and finishing are 375 and 85, respectively. Write a system of linear inequalities that represents this situation. Use the following variables: Use x for the number of tables and y for the number of chairs manufactured in a day

Assembly: _______ (> or =)
Finishing: _______ (, or =)

User XenoPuTtSs
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Final answer:

The system of linear inequalities representing the situation are: Assembly: 12x + 6y ≤ 375 and Finishing: 4x + y ≤ 85. A system of linear inequalities representing the labor hour constraints for assembling and finishing tables and chairs at a furniture manufacturing company is 12x + 6y <= 375 for assembly and 4x + y <= 85 for finishing, where x is the quantity of tables and y is the quantity of chairs.

Step-by-step explanation:

To represent the given situation as a system of linear inequalities, we can use the following variables:

x = number of tables manufactured in a day

y = number of chairs manufactured in a day

Based on the information given, we can write the following inequalities:

Assembly: 12x + 6y ≤ 375 (labor hours available for assembly)

Finishing: 4x + y ≤ 85 (labor hours available for finishing)

These inequalities ensure that the total labor hours for assembly and finishing do not exceed the given limits.

A system of linear inequalities representing the labor hour constraints for assembling and finishing tables and chairs at a furniture manufacturing company is 12x + 6y <= 375 for assembly and 4x + y <= 85 for finishing, where x is the quantity of tables and y is the quantity of chairs.

To create a system of linear inequalities for this situation, we'll consider the labor hours required for the assembly and finishing of tables and chairs, as well as the maximum labor hours available per day for these processes. The labor hours required for the assembly and finishing of a table are 12 and 4 respectively, and for a chair, they are 6 and 1 respectively. We use x for the number of tables and y for the number of chairs manufactured in a day.

With the given constraints in assembly and finishing, the inequalities are as follows:

Assembly: 12x + 6y ≤ 375

Finishing: 4x + y ≤ 85

The inequalities established here govern the production capacity of the furniture manufacturing company in terms of labor resource management.

User Toddleson
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