SOLUTION: 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​ ov

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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): You can put this solution on YOUR website!
Your keyboard doesn't have a comma?
Answer by ikleyn(52767)   (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.

---------------------

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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