Optimization Problem

[bhavik210]

Hello, this is not a direct optimization problem, I want to utilize it for a design project I am doing. I have gotten a foundation of it; however, I do not know how to start it. I have simplified it to make it easier.

So we are given a space of 74 meters x 57 meters (Total area of 4218m^2)

However, I need space for the parking aisles so the total area available is around 3630m^2

There are two types of development we are allowed to build, commercial and residential

Commercial, each unit is to be exactly 93m^2 in area, out of the total area of commercial units, 10% of the space is to be used for general purposes. For every 100m^2 of commercial area, there should be two parking spots.

I had gotten this equation:

f(x) = 93x + (93x)(0.1) The " (93x)(0.1) represents 10% general space
f(x) = 93x + 9.3x
f(x) = 102.3x

Residential, each unit is to be exactly 93m^2 in area, out of the total area of residential units, 10% of the space is to be used for general purposes. For every residential unit, there should be one parking

I had gotten this equation:

f(x) = 93x + (93x)(0.1) The " (93x)(0.1) represents 10% general space
f(x) = 93x + 9.3x
f(x) = 102.3x

Parking dimensions: 3m x 8m (24m^2). I was thinking about slant parking but for now I will assume regular parking for the sake of simplicity.

 

[JeffM]

Hello, this is not a direct optimization problem, I want to utilize it for a design project I am doing. I have gotten a foundation of it; however, I do not know how to start it. I have simplified it to make it easier.

So we are given a space of 74 meters x 57 meters (Total area of 4218m^2)

However, I need space for the parking aisles so the total area available is around 3630m^2

There are two types of development we are allowed to build, commercial and residential

Commercial, each unit is to be exactly 93m^2 in area, out of the total area of commercial units, 10% of the space is to be used for general purposes. For every 100m^2 of commercial area, there should be two parking spots.

I had gotten this equation:

f(x) = 93x + (93x)(0.1) The " (93x)(0.1) represents 10% general space
f(x) = 93x + 9.3x
f(x) = 102.3x

Residential, each unit is to be exactly 93m^2 in area, out of the total area of residential units, 10% of the space is to be used for general purposes. For every residential unit, there should be one parking

I had gotten this equation:

f(x) = 93x + (93x)(0.1) The " (93x)(0.1) represents 10% general space
f(x) = 93x + 9.3x
f(x) = 102.3x

Parking dimensions: 3m x 8m (24m^2). I was thinking about slant parking but for now I will assume regular parking for the sake of simplicity.

There are several problems with your "question." The first is that there is no specific question asked. The second is that I at least cannot quite comprehend what is being said, partly because I suspect x is being used to represent two different variables.

I have some experience in applying math to complex, concrete, practical problems. One of the first tasks is to eliminate irrelevant details, but that is more art than science and requires a thorough understanding of the problem. Here is what I think I understand about the problem.

You have an area of fixed size (presumably rectangular) = a. This is the area to be developed.

You have two types of unit, I and II, each with an area of fixed and equal (presumably rectangular) size = b. This is the size of each unit.

For each unit of either type, an additional (presumably rectangular) area is required of fixed size = 0.1b. This is common area per unit.

For each unit of type I, you need an additional area of c. Parking.

For each unit of type II, you need an additional area of 2c. Parking.

Number of units of type I = x.

Number of units of type II = y.

x(1.1b + c) + y(1.1b + 2c) = a. Is that your model?

What question do you want to ask the model?