$\"\"$

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a.

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The vector $\"\"$ represents number of men $\"\"$ s basketballs and women $\"\"$ s basketballs.

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The vector $\"\"$ represents prices of the two types of basket balls.

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The dot product of $\"\"$ and $\"\"$ is $\"\"$ .

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If two vectors $\"\"$ and $\"\"$ are orthogonal to each other, then their dot product $\"\"$ is equal to zero.

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$ \ \

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Since $\"\"$ , the vectors $\"\"$ and $\"\"$ are not orthogonal.

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$\"\"$

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b.

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The total revenue is the sum of revenue of men $\"\"$ s basketballs and revenue of women $\"\"$ s basketballs.

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The product of the number of men’s basketballs and the price of one men’s basketball is

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$\"\"$ .

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The product of the number of women’s basketballs and the price of one women’s basketball is

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$\"\"$ .

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The dot product represents the sum of these two numbers.

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The total revenue that can be made by selling all of the basketballs is

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$\"\"$ .

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The total revenue that can be made by selling two types of basketballs is $\"\"$ .

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$\"\"$

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(a).

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Vectors $\"\"$ and $\"\"$ are not orthogonal.

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(b).

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The total revenue that can be made by selling two types of basketballs is $\"\"$ .