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each week in the cutting department, 3030 hours in the assembly department, and

ID: 3195561 • Letter: E

Question

each week in the cutting department, 3030 hours in the assembly department, and 2480 in the finishing A furniture factory has 1590 machine hours department Manufacturing a chair requires o 2 hour of cutting, 0.8 hour of assembly, and 0.5 hour of finishing A cabinet requires 0.5 hour of cutting, 0.1 hour of assembly, and 0.2 hour of finishing A buffet requires 0.3 hour of cutting, 0.9 hour of assembly, and 0 8 hour of finishing. How many chairs, cabinets, and buffets should be produced in order to use all the available production capacity? Write a linear system of equations. Let x represent the number of chairs created, y represent the number of cabinets created, and z represent the number of buffets created. Choose the correct answer below O A. 0.3x y 02z-1590 B. 0.5x+0.2y Z -3030 02x+050 8y +02z = 1590 0.3x+0.2y 0.9z 2480 05x+020 3y + 05z = 3030 0.2x + 0.5y + 0.3 1590 0.8x+0.1y+0.9z 3030 0.5x+0.2y+ 0.8z 2480 02x+05y+03z = 3030 08x+01y+ 0.9z- 2480 05x+02y + 0 8z = 1590 OC. OD,

Explanation / Answer

Information given:

Machine hours in Cutting department = 1590

Machine hours in Assembly department = 3030

Machine hours in Finishing department = 2480

For manufacturing,

A chair requires: 0.2 hours of Cutting, 0.8 hours of Assembly, and 0.5 hours of Finishing.

A cabinet requires: 0.5 hour of Cutting, 0.1 hour of Assembly, and 0.2 hours of Finishing.

A buffet requires: 0.3 hours of Cutting, 0.9 hours of Assembly, and 0.8 hours of Finishing.

Now, let's say 'x' chairs, 'y' cabinets, and 'z' buffets are to be made in order to use all the production capacity available.

Therefore, for 'x'chairs, 'y' cabinets, and 'z' buffets need 1590 hours from Cutting department, 3030 hours from Assembly department, 2480 hours from Finishing department.

That leads us to the following linear equations:

0.2x+0.5y+0.3z=1590

0.8x+0.1y+0.9z=3030

0.5x+0.2y+0.8z=2480

The answer which is option B.

Finally, we remained with 3 equations and 3 unknowns which are easily solvable.

By solving above three linear equations we get :

the number of chairs(x)=1800

the number of cabinets(y)=1500

the number of buffets(z)=1600.