Question

El Pesa Canto labs is an organization that provides research facilities to researchers in various fields. They plan to develop a large research facility that offers lab space to researchers in the fields of engineering and Chemistry. There are two types of labs: those that are stocked with equipment, whereby researchers have the resources available to them; and those that are empty workspaces, where researchers can bring their own equipment to conduct their studies in an area designed for their field in terms of safety standards and dimensions. The table below illustrates the details of these labs with regards to the cost of building each lab, and price for which each lab is rented to researchers.

	Cost to build each Lab	Price rented out per month
Non-Equipped Chemistry Labs	$190,000	$10,000
Non-Equipped Engineering Labs	$710,000	$15,000
Equipped Chemistry Labs	$700,000	$45,000
Equipped Engineering Labs	$1,500,000	$110,000

Given that El Psy Congroo has a maximum budget of $1,000, 000,000 (i.e. 1 billion dollars) to build these labs, they also have a few additional requirements:

• There should be at least twice the number of chemistry labs as opposed to engineering labs.                                                                                                                 
• Equipped Engineering labs should be at least three times less that Non-Equipped Engineering labs.
• Equipped Chemistry labs should be at least two times less than Non-Equipped Chemistry labs.
• There should be at least 25 chemistry labs (Equipped or unequipped) in total, but no more than 40.

Develop the LP Model for this question and use the solver to attain the optimal solution.

      

Answer 1

Let X1,X2,Y1,Y2 are the variables representing Non equipped chemistry labs, equipped labs, Non equipped engineering labs and Equipped engineering labs respectively

Maximize revenue of the labs can be represented s follows

Z= $10000X1+$15000Y1+$45000X2+$110000Y2 subject to constraints as follows

Budget shall not be more than $1,000, 000,000

$190000X1+$710000Y1+$700000X2+$1500000Y2= $1,000, 000,000

There should be at least twice the number of chemistry labs as opposed to engineering labs

Y1+Y2 ≥ 2(X1+X2)

Equipped Engineering labs should be at least three times less that Non-Equipped Engineering labs.

Y2 ≥ 3Y1

Equipped Chemistry labs should be at least two times less than Non-Equipped Chemistry labs.

X2 ≥ 2X1

There should be at least 25 chemistry labs (Equipped or unequipped) in total, but no more than 40

X1+X2 ≥ 25

X1+X2 ≤ 40

By solving the above equations using solver in excel sheet

X1=8.33

Y1=8.2

X2=16.67

Y2=657.83

revenue =$73195000