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.

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

Oh, go ahead, solve it for fun !

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).

To construct a linear program for this situation, let's define the variables and identify the objective function and constraints.

Variables:
Let's define two variables:
- x: represents the number of one-person rooms to be refurbished.
- y: represents the number of two-person rooms to be refurbished.

Objective Function:
The objective is to maximize the number of people accommodated. Since each one-person room accommodates 1 person and each two-person room accommodates 2 people, the objective function can be written as:
Maximize: x + 2y

Constraints:
1. The hotel has a maximum capacity of 100 rooms. So the total number of refurbished rooms cannot exceed 100:
x + y ≤ 100

2. The hotel has a maximum of 270 hours available for service. Each one-person room requires 2.5 hours of service and each two-person room requires 3 hours of service. Therefore, the total number of hours for service cannot exceed 270:
2.5x + 3y ≤ 270

3. At least 35 rooms must be one-person rooms, so:
x ≥ 35

4. At least 20 rooms must be two-person rooms, so:
y ≥ 20

5. Both x and y should be non-negative since the number of rooms cannot be negative:
x ≥ 0
y ≥ 0

By formulating the linear program with the above variables, objective function, and constraints, we can determine the optimal number of rooms of each type to maximize the number of people accommodated.