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Math Help - Expected Profits

  1. #1
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    Expected Profits

    Hello!

    I am having trouble with a stats question i was given. I'll write the question first, and then explain what I have done to try and solve it.

    Q) Suppose the monthly demand for tomatoes (a perishable good) in a small town is random. With probability 1/3, demand is 40; with probability 2/3, demand is 200. You are the only producer of tomatoes in this town. Tomatoes sell for a xed price of $1, cost $0.50 to produce, and can only be sold in the local market. If you produce 60 tomatoes, what is your expected profit?



    My first instinct tells me the two variables in this question are the demands.. one variable being a demand of 40, the other variable being a demand of 200 (im not even sure if this part is right, but lets move on).

    The way I tried to start was:

    Expected profit = (40*(1/3)) + (200*(2/3)) = 146.67

    This is all I can think of, but I am assuming I have to use the 60 tomatoes, with their price ($1) and cost (50 cents) as well, I just don't know what to do with them.

    Any pointers would be great! thank you
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  2. #2
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    Re: Expected Profits

    youve calculated the expected revenue, not the expected profit.

    you need to deduce the costs in each scenario, which are 60*0.5 = 30.
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  3. #3
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    Re: Expected Profits

    Ahhh, so if my expected revenue is $146.67.....

    To get expected profit, its just expected revenue - costs, so:

    146.67 - 30 = $116.67

    Thank you very much!
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