$\"\"$

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(a)

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Josh is working part-time to pay his college expenses.

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Josh delivery pizza for $\"\"$ per hour plus tips, his run about $\"\"$ per hour.

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The objective function is $\"\"$ .

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The josh can do no more than $\"\"$ hours per week during his class schedule, hence $\"\"$ and $\"\"$ .

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Josh tutors in the math lab for $\"\"$ the math lab is open only $\"\"$ hour daily.

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$\"\"$

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

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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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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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The josh make the money is is $\"\"$ .

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$\"\"$

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(a) The objective function is $\"\"$ and 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 josh make the money is is $\"\"$ .