Linear Programming

Question

You have to purchase some kitchen cabinets. You realize that Cabinet X expenses $10 for every unit, obliges six square feet of floor space, and holds eight cubic feet of records. Cabinet Y costs $20 for every unit, obliges eight square feet of floor space, and holds twelve cubic feet of storage. You have been given $140 for this buy, however you don't need to use that much. The workplace has space for close to 72 square feet of cabinets. What number of which model would it be advisable for you to purchase, keeping in mind the end goal to boost storage volume?

You have to purchase some kitchen cabinets. You realize that Cabinet X expenses $10 for every unit, obliges six square feet of floor space, and holds eight cubic feet of records. Cabinet Y costs $20 for every unit, obliges eight square feet of floor space, and holds twelve cubic feet of storage. You have been given $140 for this buy, however you don't need to use that much. The workplace has space for close to 72 square feet of cabinets. What number of which model would it be advisable for you to purchase, keeping in mind the end goal to boost storage volume?

Answer 1

Say,

The no of X cabinets= x

The no of Y cabinets = y

 

We have to maximize the storage volume

 

So, the objective function=

Max 8x+12y

 

As per given data the constraints are---

 

10x+20y <=140

 

 6x+8y    <=72

 

We should plot these constraints on a graph and obtain the extreme points.

 

The extreme points are as follows-----

 

(0,7).  ,(12,0).   (8,3)

 

let us find the values of objective functions at these extreme points

 

at (0,7).      ---- =74

at (12,0)     ----- =96

at (8,3).      ----- =100

 

So, (8,3) is the optimal point.

 

Value of maximum volume =100 cu Ft