19.

20.

21.

18595

3 D 10673
Add slack variables to the following linear programming problem and write the initial simplex
tableau:

Maximize Z = 3x, + 2x5 +x

subject to ‏د2‎ + छ + 8 < 150
2201 + 229 + 853 < 200

2x1 + 3 + 8 < 320

and 1, 2, 9 = 0.

(5 x 5 = 25 marks)
Section C

Answer any one question.
The question carries 11 marks.

Assume that the demand of an item A increases as the price decreases. If the weekly demand for
A is q (in dollar $) and the price is p then suppose that they are related by the linear relation
D (p) = 9 -0.7ರ(.
(a) Find the quantity demanded at a price of $ 5.25 per item and at a price of $3.75 per item.
(0) It is also noticed that the quantity of item A supplied decreased as the price decreased.

If price p and supply q are related by the linear function S (p) = 0.75q, find the quantity
supplied at a price of $ 5.25 per item and at a price of $ 3.00 per item.

(c) Graph both functions D (p) and S (p) on the same axes.
Solve the problem using simplex method :

Maximize Z = 12x, + 15x, + 5x,

subject to 2x, + 2x) +23 <8
2] + 49 + 38 < 12
xy 2 0, x9 2 0, x3 >0.

(1 x 11 = 11 marks)

18595