Question

A manager of an Office contemplates to buy 2 filing cabinets (X and Y): X holds 8 cubic feet of files, requires 6 sq feet of floor space, and costs $10 per unit while Y holds 12 cubic feet of files, requires 8 sq feet of floor space, and costs $20 per unit.
The manager has $140 to spend (and need not spend it all). The Office has no more than 72 sq feet of cabinet space.
How many of which cabinets (X and Y) should the manger buy to maximize file storage volume?
Write the mathematical formulation of this LP problem, find the feasible region graphically (by drawing the constrains), and then suggest a solution
(i) by trial and error method, and
(ii) graphically.

Answer 1

Manager wants to maximize the storage volume, here, X holds 8 cubic feet of files, and Y holds 12 cubic feet of files.

Number of X cabins = X1

Number of Y Cabins =X2

Maximize Objective function Z=8*X1+12*X2

Constraints are as stated below:

6*X1+8*X2=<72

And

10*X1+20*X2=<140

X1 and X2>=0

6*X1+8*X2=<72

X1	X2
0	9
12	0

10*X1+20*X2=<140

X1	X2
0	7
14	0

Graph:

Feasible region is shown within the green shed

here, optimal solution Z or objective function =100 cubic feet

Number of X cabins = X1=8

Number of Y Cabins =X2=3