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Math Help - Solve word prob using linear inequalities??

  1. #1
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    Solve word prob using linear inequalities??

    You are the manager of a small appliance store. You need to order two types of microwave ovens. The deluxe model costs you $500 and the basic model costs you $300. The profit for the deluxe model is $200 while the profit for the basic model is $50. You would like to sell a minimum of 100 microwaves and make a total profit of at least $8000. How many of each model should you order to minimize the costs?
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  2. #2
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    Quote Originally Posted by katt View Post
    You are the manager of a small appliance store. You need to order two types of microwave ovens. The deluxe model costs you $500 and the basic model costs you $300. The profit for the deluxe model is $200 while the profit for the basic model is $50. You would like to sell a minimum of 100 microwaves and make a total profit of at least $8000. How many of each model should you order to minimize the costs?
    Say you buy D deluxe models and B basic models.

    You want to sell at least 100 microwaves, so B+D \geq 100
    Your profit is at least 8000 so 50B + 200D > \geq 8000

    These simultaneous equations give D \geq 20, B \geq 80.

    So in order to satisfy both conditions, you must sell at least 20 deluxe models and 80 basic models. But since you are asked to minimize the cost, we shall assume you are not to sell any more than that. So you should sell 20 deluxe models and 80 basic models.
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  3. #3
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    Quote Originally Posted by Unenlightened View Post
    Say you buy D deluxe models and B basic models.

    You want to sell at least 100 microwaves, so B+D \geq 100
    Your profit is at least 8000 so 50B + 200D > \geq 8000

    These simultaneous equations give D \geq 20, B \geq 80.

    So in order to satisfy both conditions, you must sell at least 20 deluxe models and 80 basic models. But since you are asked to minimize the cost, we shall assume you are not to sell any more than that. So you should sell 20 deluxe models and 80 basic models.
    also can you tell me how to place it in an linear inequality for final answer? an linear inequality equation for graphing the solution also?
    Last edited by katt; November 21st 2009 at 01:58 PM. Reason: spelling
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