Question 1111749: A company produces alarm clocks. During the regular workweek, the labor cost for producing one clock is $2
.00.
However, if a clock is produced on overtime, the labor cost is $3
.00.
Management has decided to spend no more than a total of $23 comma 000
per week for labor. The company must produce 10 comma 000
clocks this week. What is the minimum number of clocks that must be produced during the regular workweek?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
Answer by ikleyn(52765)  (Show Source):
You can put this solution on YOUR website! .
Let x = number of clocks that produced during the regular workweek,
y = number of clocks that produced on overtime.
Then you have these simultaneous equation and inequality
x + y = 10000 (1)
2x + 3y <= 23000 (2)
Multiply eq(1) by (20 (both sides). Keep inequality (2) as is. You will get
2x + 2y = 20000, (3)
2x + 3y <= 23000. (4)
You can transform left part of (4) in this way
2x + 3y = (2x + 2y) + y = 20000 + y, replacing 2x + 2y by 20000 based on (3). Then you get
20000 + y <= 23000, or, equivalently,
y <= 23000 - 20000 = 3000.
Since y <= 3000, then (1) implies x = 10000 - y >= 10000 - 3000 = 7000.
So, your answer is x >= 7000.
Answer. The minimum number of clocks that must be produced during the regular workweek is 7000.
SOLVED.
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In your condition, every occurrence " comma " can be and must be replaced by "".
In other words, it can be OMITTED, to everybody' satisfaction.
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