SOLUTION: A manufacturing company makes two sizes of gizmos: the large size and the small size. It takes 25 minutes of machine time and an hour and 10 minutes of labor to make the small size

Question 577874: A manufacturing company makes two sizes of gizmos: the large size and the small size. It takes 25 minutes of machine time and an hour and 10 minutes of labor to make the small size, and 42 minutes of machine time and 1 hour and 17 minutes of labor to make the large size. Each day the company has 56 hours of labor time and 24.5 hours of machine time available. If all the available time is used, how many gizmos of each size can be made per day?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A manufacturing company makes two sizes of gizmos: the large size and the small size.
It takes 25 minutes of machine time and an hour and 10 minutes of labor to make the small size,
and 42 minutes of machine time and 1 hour and 17 minutes of labor to make the large size.
Each day the company has 56 hours of labor time and 24.5 hours of machine time available.
If all the available time is used, how many gizmos of each size can be made per day?
:
Let b = no. of big size made
let s = no. of small size
:
we can do everything in minutes
1 hr 10 min = 70 minutes
1 hr 17 min = 77 min
56*60 = 3360 min, total labor time
24.5*60 = 1470 min, total machine time
:
Machine time equation
42b + 25s = 1470
:
The labor equation:
77b + 70s = 3360
:
to use elimination here, multiply the machine equation by 14, the labor equation by 5
588b + 350s = 20580
385b + 350s = 16800
-------------------subtraction eliminates s, find b
203b = 3780
b =
b = 18.62 ~ 18 big items, assuming we have to have an integer here
and
42(18) + 25s = 1470
756 + 25s = 1470
25s = 1470 - 756
25s = 714
s =
s = 28.56 ~ 28 small items
:
:
Check this in the total labor equation
77(18) + 70(28) =
1386 + 1960 = 3346 min leaving 3360 - 3346 = 14 unused minutes
:
Check using the machine equation
42(18) + 25(28) =
756 + 700 = 1456 min. leaving 1470 - 1456 = 14 min unused

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