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Math Help - Minimize Driver Cost

  1. #1
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    Minimize Driver Cost

    I'm getting tired of these questions! urrrrggghh. High school needs a better system for students to have questions answered... sorry guys for repeatedly posting questions on here today.

    24. Stan needs to move some excess topsoil from his farm. He can hire a dump
    truck and a driver for $60/h. The driver will take 30 min to deliver a load of
    topsoil and return to the farm. One person will take 40 h to load the truck
    with soil. Labourers get $18/h (whether they are loading the truck with soil
    or waiting for the truck to return). How many labourers should Stan hire to
    minimize the cost per load? What is the minimum cost?



    I'm supposedly waayyyy off. Answer should be 5.
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  2. #2
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    Quote Originally Posted by mike_302 View Post
    I'm getting tired of these questions! urrrrggghh. High school needs a better system for students to have questions answered... sorry guys for repeatedly posting questions on here today.

    24. Stan needs to move some excess topsoil from his farm. He can hire a dump
    truck and a driver for $60/h. The driver will take 30 min to deliver a load of
    topsoil and return to the farm. One person will take 40 h to load the truck
    with soil. Labourers get $18/h (whether they are loading the truck with soil
    or waiting for the truck to return). How many labourers should Stan hire to
    minimize the cost per load? What is the minimum cost?



    I'm supposedly waayyyy off. Answer should be 5.
    We're probably making the same mistake if your answer is wrong because I agree with you.

    Let the number of loads be n and number of workers be x.

    Driver:

    Number of hours of truck driver: \frac{n}{2} + \frac{40}{x} n.

    Cost of driver: \left( \frac{n}{2} + \frac{40}{x} n\right) 60.

    Cost of driver per load: \left( \frac{1}{2} + \frac{40}{x}\right) 60 = 30 + \frac{2400}{x}.


    Workers:

    Number of worker hours: \frac{n}{2} + \frac{40}{x} n.

    Cost of workers: \left( \frac{n}{2} + \frac{40}{x} n\right) 18x.

    Cost of workers per load: \left( \frac{1}{2} + \frac{40}{x}\right) 18x = 720 + 9x.


    Cost per load: C = 30 + \frac{2400}{x} + 720 + 9x = 750 + 9x + \frac{2400}{x}.
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  3. #3
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    well, the book's answer is 5 labourers... @ 5 labourers, you're looking at 8 hours of a dump truck waiting around @ $60 per hour... Sure, you arent paying a lot of labourers, but you are paying the few you have, a lot of hours, and you are paying the most expensive component (the truck) a HECK of a lot more for a lot longer... Something tells me that, even if our answer isn't right, the book's isn't either... At the very least. But in that case, ours is likely right.
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