$\"\"$

\

Consider the number of cars are $\"\"$ and the number of buses are $\"\"$ .

\

The area of parking lot is $\"\"$ and a car require $\"\"$ space and a bus require $\"\"$ space.

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Hence, the inequality is $\"\"$ .

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The attendant can handle no more than $\"\"$ vehicles , if it costs $\"\"$ to park a car and $\"\"$ to park a bus.

\

Hence, the objective function is $\"\"$ .

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The inequaity is $\"\"$ .

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The number of cars and number of buses should not be negative.

\

Therefore, the constraints are

\

$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Graph :

\

Graph the inequalities and shade the required region.

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$\"\"$

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Note : The shaded region is the set of solution points for the objective function.

\

Observe the graph,

\

Tabulate the solutions of each of two system of inequalities and obtain the intersection points.

\ \

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\

System of boundary

\

equations

\

\

$\"\"$

\

$\"\"$

\

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$\"\"$

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$\"\"$

\

\

$\"\"$

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$\"\"$

\

\

$\"\"$

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$\"\"$

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Solution (vertex points)

\"\"

\"\"

\"\"

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$\"\"$

\

\

$\"\"$

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Find the value of objective function at the solution points.

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At point $\"\"$ , $\"\"$ .

\

At point $\"\"$ , $\"\"$ .

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At point $\"\"$ , $\"\"$ .

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At point $\"\"$ , $\"\"$ .

\

Observe the values of $\"\"$ ,

\

The maximum value of $\"\"$ is $\"\"$ when $\"\"$ and $\"\"$ .

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The minimum value of $\"\"$ is $\"\"$ when $\"\"$ and $\"\"$ .

\

Hence, the number of buses are $\"\"$ and number of cars are $\"\"$ .

\

Therefore, the correct choice is $\"\"$ .

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$\"\"$

\

The correct choice is $\"\"$ .