# Finite Math

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Construct a linear program for the following situation. Do not solve.

A hotel is refurbishing its rooms, each type of which will accommodate either one or two persons. A one-person room requires 2.5 hours of service each day and a two-person room requires 3 hours of service each day. the hotel is able to refurbish up to 100 rooms and has available up to 270 hours a day for service. At least 35 rooms must be one-person rooms and at least 20 rooms must be two-person rooms. How many room of each type should be refurbished in order to accommodate the most people? Identify/name your variables. Give the objective function. Give the constraints.

• Finite Math -

n = 1 person rooms
m = 2 person rooms

P = n + 2 m = objective to maximize number of people

constraints
n>/= 35
m>/= 20
n+m </= 100
2.5 n + 3 m </= 270

• Finite Math -

Oh, go ahead, solve it for fun !

• Finite Math -

It is just like word problems back in algebra. Define variable names. Read each sentence and convert it into an expression, usually an inequality. Call the thing you want to maximize or minimize the objective function. Sketch a graph labeling which side of each constraint line is allowed. Look at the value of your objective function at every corner of the graph. Pick the best one (max or min of objective function) depending on which you are looking for (max or min).

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