A company has factories located in New Jersey, Ohio, and Georgia where it manufactures handbags, shoes, and belts. How many days should the company operate each factory in order to exactly fill the order of 2150 handbags, 2300 shoes and 2500 belts? Use the information below.
Handbags
# of handbags produced per day
New Jersey 10
Ohio 70
Georgia 60
Shoes
# of shoes produced per day
New Jersey 20
Ohio 50
Georgia 80
Belts
# of belts produced per day
New Jersey 40
Ohio 30
Georgia 90
x = number of days to operate NJ
y = number of days to operate OH
z = number of days to operate GA
10x + 70y + 60z = 2150 (Handbags)
20x + 50y + 80z = 2300 (Shoes)
40x + 30y + 90z = 2500 (Belts)
Solve for x, y, and z simultaneously
If you want, post back with your answer and I'll check.
To determine how many days each factory should operate to fill the order, we need to calculate the production capacity of each factory for each product.
First, let's calculate the production capacity for handbags:
- New Jersey: 10 handbags per day
- Ohio: 70 handbags per day
- Georgia: 60 handbags per day
Next, let's calculate the production capacity for shoes:
- New Jersey: 20 shoes per day
- Ohio: 50 shoes per day
- Georgia: 80 shoes per day
Finally, let's calculate the production capacity for belts:
- New Jersey: 40 belts per day
- Ohio: 30 belts per day
- Georgia: 90 belts per day
Now, we need to determine how many days each factory should operate to exactly fill the order of 2150 handbags, 2300 shoes, and 2500 belts.
For handbags:
- New Jersey: 2150 handbags / 10 handbags per day = 215 days
- Ohio: 2150 handbags / 70 handbags per day = 31 days
- Georgia: 2150 handbags / 60 handbags per day = 36 days
For shoes:
- New Jersey: 2300 shoes / 20 shoes per day = 115 days
- Ohio: 2300 shoes / 50 shoes per day = 46 days
- Georgia: 2300 shoes / 80 shoes per day = 29 days
For belts:
- New Jersey: 2500 belts / 40 belts per day = 62.5 days (round up to 63 days)
- Ohio: 2500 belts / 30 belts per day = 83.33 days (round up to 84 days)
- Georgia: 2500 belts / 90 belts per day = 27.78 days (round up to 28 days)
Therefore, to exactly fill the order of 2150 handbags, 2300 shoes, and 2500 belts, the company should operate each factory for the following number of days:
- New Jersey: 215 days for handbags, 115 days for shoes, and 63 days for belts.
- Ohio: 31 days for handbags, 46 days for shoes, and 84 days for belts.
- Georgia: 36 days for handbags, 29 days for shoes, and 28 days for belts.