Wazzamanutd
New member
- Joined
- Jun 5, 2018
- Messages
- 2
Hello all, I was hoping you could help me answer the following questions.
I am to use the Gauss-Jordan elimination method but I am struggling.
PROBLEM 1:
A furniture manufacturer makes sofas, chairs, and ottomans. The accompanying table gives the number of hours of labor required for the carpentry and upholstery that goes into each item. Suppose that each day, 407407
labor-hours are available for carpentry and 459459
labor-hours are available for upholstery. Give three different combinations for the number of each type of furniture that can be manufactured each day.
If 4545
chairs are manufactured, how many ottomans and sofas can be manufactured?
PROBLEM 2:
A chemical manufacturer wants to lease a fleet of 2626
railroad tank cars with a combined carrying capacity of 434 comma 000434,000
gallons. Tank cars with three different carrying capacities are available: 7 comma 0007,000
gallons, 14 comma 00014,000
gallons, and 28 comma 00028,000
gallons. How many of each type of tank car should be leased?
Let x1
be the number of cars with a 7 comma 0007,000
gallon capacity, x2
be the number of cars with a 14 comma 00014,000
gallon capacity, and x3
be the number of cars with a 28 comma 00028,000
gallon capacity. Select the correct choice below and fill in the answer boxes within your choice.
A. There is no solution.
B. The unique solution is x 1 equalsx1=nothing,
x 2 equalsx2=nothing,
and x 3 equalsx3=nothing.
(Simplify your answers.)
C. There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x 1 equalsx1=nothingtplus+(nothing),
x 2 equalsx2=nothingtplus+(nothing),
and x 3 equalsx3=t
for nothingless than or equals≤tless than or equals≤
nothing
FFFF
I am to use the Gauss-Jordan elimination method but I am struggling.
PROBLEM 1:
A furniture manufacturer makes sofas, chairs, and ottomans. The accompanying table gives the number of hours of labor required for the carpentry and upholstery that goes into each item. Suppose that each day, 407407
labor-hours are available for carpentry and 459459
labor-hours are available for upholstery. Give three different combinations for the number of each type of furniture that can be manufactured each day.
| Ottoman | Sofa | Chair | |
| Carpentry | 1 hour | 33 hours | 66 hours |
| Upholstery | 33 hours | 66 hours | 33 hours |
chairs are manufactured, how many ottomans and sofas can be manufactured?
PROBLEM 2:
A chemical manufacturer wants to lease a fleet of 2626
railroad tank cars with a combined carrying capacity of 434 comma 000434,000
gallons. Tank cars with three different carrying capacities are available: 7 comma 0007,000
gallons, 14 comma 00014,000
gallons, and 28 comma 00028,000
gallons. How many of each type of tank car should be leased?
Let x1
be the number of cars with a 7 comma 0007,000
gallon capacity, x2
be the number of cars with a 14 comma 00014,000
gallon capacity, and x3
be the number of cars with a 28 comma 00028,000
gallon capacity. Select the correct choice below and fill in the answer boxes within your choice.
A. There is no solution.
B. The unique solution is x 1 equalsx1=nothing,
x 2 equalsx2=nothing,
and x 3 equalsx3=nothing.
(Simplify your answers.)
C. There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x 1 equalsx1=nothingtplus+(nothing),
x 2 equalsx2=nothingtplus+(nothing),
and x 3 equalsx3=t
for nothingless than or equals≤tless than or equals≤
nothing
FFFF