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How to find maximums and minimums in Algebra 2.?

Here is one of the questions on my Homework.

A department store is planning to hire up to 24 temporary employees for a tent sale. Experienced workers will be paid $20 per hour and inexperienced workers $15 per hour. The company can pay up to $400 per hour for the temporary employees. An experienced worker produces 1.5 times the profit of an inexperienced worker. How many of each type should be hired?

x = experienced workers
y= inexpereinced workers
x+y=24
solve for either x or y, i’ll do x
x=24-y

set up another equation now
y($15) + (24-y)($20)=$400
distribute
15y + 480 -20y =400
solve for y
-5y = – 80
5y = 80
y=16
now you know they need 16 inexperienced workers
to get experienced workers plug 16 into the equation you created earlier
x = 24 -y
so
x=24-16
x=8
they need 8 experienced workers

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4 Responses to “How to find maximums and minimums in Algebra 2.?”

  1. Novy Says:
    February 9th, 2010 at 5:21 pm

    This is an extremely badly worded question.

    Obviously, to maximize profit, you want more experienced workers. It does not mention that the profit is affected by how much you pay them. Thus you want how ever many experienced workers you can afford without exceeding 24, or 24 max if you can afford them. (The company says they want "UP TO" 24 workers, meaning they can take less than that).

    Thus 400 / 20 = 20

    So 20 experienced workers, 0 inexperienced workers.

    Be warned, if this is for your homework, this is most likely not what the problem wanted you to do although its what it asked.
    References :

  2. RB Says:
    February 9th, 2010 at 5:40 pm

    x = experienced workers
    y= inexpereinced workers
    x+y=24
    solve for either x or y, i’ll do x
    x=24-y

    set up another equation now
    y($15) + (24-y)($20)=$400
    distribute
    15y + 480 -20y =400
    solve for y
    -5y = – 80
    5y = 80
    y=16
    now you know they need 16 inexperienced workers
    to get experienced workers plug 16 into the equation you created earlier
    x = 24 -y
    so
    x=24-16
    x=8
    they need 8 experienced workers
    References :

  3. hayharbr Says:
    February 9th, 2010 at 5:48 pm

    You have to raph all the inequalities in the problem, find the coordinates of the polygon formed, then plug those coordinates in (one pair at a time) to the profit formula

    x = experienced
    y = inexperienced

    x ≥ 0
    y ≥ 0
    x + y ≤ 24
    20x + 15y ≤ 400

    and P = some constant times (x + 1.5y) but the constant doesn’t matter
    References :

  4. ironduke8159 Says:
    February 9th, 2010 at 6:22 pm

    x = # of experienced workers
    y = # of inexperienced workers
    x + y = 24
    Cost = 20x + 15y = 400 –> 4x + 3y = 80
    Profit = Revenue – Cost
    No way to compute revenue with data given.

    References :

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