Math Algebra

Question::

You are about to take a test that contains questions of type A worth 4 point and of type B worth 7 points. You must andwer at least 5 of type A and 3 of type B, but time restricts answering more than 10 of either type. Intotal, you can answer no more than 18. How many of each type of question must you answer, assuming all of your answers are correct, to maximize you score? What is the maximum score?

...im thinking the answer is 8 of type A and 10 of type B, but im not sure... please help!! Thanks!!

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  1. maximize 4A+7B subject to
    A >= 5
    B >= 3
    A <= 10
    B <= 10
    A+B <= 18

    A=8
    B=10
    score = 102

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