$\"\"$

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(a)

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Let $\"\"$ be the cost of physicals as $\"\"$ and $\"\"$ is a checkup costs $\"\"$ .

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The objective function is $\"\"$ .

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The doctor can do no more than $\"\"$ physical per day is $\"\"$ and $\"\"$ .

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One of her tasks is to shedule appointments is $\"\"$ minutes for the checkup and $\"\"$ minutes for the physicals and clinic has $\"\"$ hours per a day.

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$\"\"$ hours in minutes is $\"\"$ .

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$\"\"$

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Therefore the constraints are

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Graph :

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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.

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Observe the graph,

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

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

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System of boundary

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equations

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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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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(c)

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Find the value of objective function at the solution points.

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

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

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

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

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Observe the values of $\"\"$ ,

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The maximum income is $\"\"$ when oliva shedule is $\"\"$ checkup and $\"\"$ physicals.

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$\"\"$

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(a) The constraints are $\"\"$ , $\"\"$ and $\"\"$ .

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(b)

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Graph :

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Graph the inequalities and shade the required region.

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$\"\"$

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(c) The maximum income is $\"\"$ when oliva shedule is $\"\"$ checkup and $\"\"$ physicals.