Question

Example 4 : A firm can produce three types of cloth say A, B and C. Three
cinds of wool are required for it, say red wool, green wool and blue wool. One unit
Length of type A cloth needs 2 yards of red wool and 3 yards of blue wool, one unit
length of type B cloth needs 3 yards of red wool, 2 yards of green wool and 2 yarós
of blue and one unit of type C cloth needs 5 yards of green wool and 4 yards of blue
wool. The firm has only a stock of 8 yards of red wool, 10 yards of green wool and
15 yards of blue wool. It is assumed that the income obtained from one unit length
of type A cloth is Rs. 3.00 of type B cloth is Rs, 5.00 and of type C doth is Rs. 4.00
(1) Formulate the problem as linear programming problem,
(ii) Determine how the firm should use the available material, so as to maximize
the income from the finished cloth,​

Answer 1

there is mistake in data

Step-by-step explanation:

A = 1R  + 2G + 3Bl

B = 2R + 3G + 4Bl

C = 3R + 4G + 1Bl

Stock  R = 14

G = 20

Bl = 14

Let say X  unit of  A  &  Y unit of B   then 14-(X + Y) units of C

14R  =  XR  + 2YR  + (14 - X - Y)3R

=> 14 = X + 2Y + 42 - 3X - 3Y

=> 2X + Y  = 28

G

20 = 2X + 3Y + 4(14 - X - Y)

=> 2X + Y  = 36

28 ≠ 36

Hence there is mistake in data

Bl

14 = 3X + 4Y + (14 - X - Y)

=> 2X + 3Y = 0

Sum of two units produced can not be Zero

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Answer 2

Answer:

length of type B cloth needs 3 yards of red wool, 2 yards of green wool and 2 yarós

of blue and one unit of type C cloth needs 5 yards of green wool and 4 yards of blue

wool. The firm has only a stock of 8 yards of red wool, 10 yards of green wool and

15 yards of blue wool. It is assumed that the income obtained from one unit length

of type A cloth is Rs. 3.00 of type B cloth is Rs, 5.00 and of type C doth is Rs. 4.00

(1) Formulate the problem as linear programming problem,

(ii) Determine how the firm should use the available material, so as to maximize

the income from the finished