Posted by **Jen** on Wednesday, December 3, 2008 at 4:09pm.

Please help...i'm totally lost with this one.

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 -
**Damon**, Wednesday, December 3, 2008 at 5:16pm
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 -
**Damon**, Wednesday, December 3, 2008 at 5:17pm
Oh, go ahead, solve it for fun !

- Finite Math -
**Damon**, Wednesday, December 3, 2008 at 6:02pm
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).

## Answer this Question

## Related Questions

- math - Help pleaseeee The Hotel Regal has 500 rooms. Currently the hotel is ...
- statistics - Consider the average available for all hotel rooms from the ...
- BUSSINESS STATISTICS - Consider the average available for all hotel rooms from ...
- math - Help please >.< The Hotel Lakewell has 450 rooms. Currently the ...
- math/algebra - I need help in solving this word problem using linear system ...
- Math - The Hotel Regal has 600 rooms. Currently the hotel is filled . The daily ...
- Pre-Calculus - The Hotel Bellville has 400 rooms. Currently the hotel is filled...
- programming - A hotel’s occupancy rate is calculated as follows: Occupancy rate...
- precalculus - The Hotel Thomasina has 500 rooms. Currently the hotel is filled...
- pre-calculus - The Hotel Florence has 550 rooms. Currently the hotel is filled...