MCL261

TUT SHEET 1

SOLVING LPP GRAPHICALLY

Q1. Answer the following:

a). What are the 4 possible types of solutions you can get for a LPP (Linear Programming Problem)?

b). Is it possible to have a bounded solution to an unbounded feasible region? If yes, give an example.

Else give a reason.

c). Can an optimal solution to a LPP exist in the interior of a feasible set?

d). Is it possible to have finitely many (>1) optimal solutions to a LPP?

Q2. Solve the following linear programming problem graphically:

Maximise Z = 4x + y

subject to

x + y ≤ 50

3x + y ≤ 90

x ≥ 0, y ≥ 0

Q3. Suppose you need to buy some cabinets for a room. There are two types of cabinets that you have

liked in the market, say X and Y . Each unit of cabinet X costs you Rs 15000 and requires 6 square feet

of floor space, and holds 8 cubic feet of files. On the other hand each unit of cabinet Y Costs Rs 12000,

requires 8 square feet of floor space and holds 12 cubic feet of files. You have been given Rs 140,000 for

this purchase, though you may not spend all. The office has room for no more than 72 square feet of cabi-

nets. How many of each model you must buy in order to maximize the storage volume? (Solve graphically)

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