What is the blend cost of spinning
The cotton in one bale must be very uniform but because of so many reasons
great variations arise. To overcome these variations it is good practice to blend as many
bales as possible to obtain a uniform yarn. The mixing of several bales together is not
only desirable but essential.
There are often opportunities in mixing to take advantage of the price factor with the blend cost of spinning. For example
by using 8 bales of the lower grade with 12 bales of somewhat higher grade, in a 20 bale
mix, the quality may be maintained, with a saving in the cost of raw cotton.
Having made the required mixing it is necessary to obtain the average price per kilogram of
the blend.
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Cost = Price x Weight
Price (P) = Cost = C
Weight W
(Price is a rate of unit weight while cost is money for total weight)
Price of a mixing;
PM = Cost of all components.
Weight of all components
PM = (CA + CB + …….…)
(WA + WB + ………)
= (PA × WA + PB X WB + ………. )
(WA + WB + ……………..)
Where;
PM = price of mixing
C = cost = price × weight
P = price (rate)
A & B are the components
Average Price of Mixing.
Question no. 1
The price of mixing component A with a weight of 20,000 kg is $ 0.70/- while the price
of component B with a weight of 2,5000 kg is $ 0.78/-. Calculate the average price of
mixing.
Solution:
PM = (CA + CB)/(WA + WB)
= (PA × WA + PB × WB)/(WA + WB)
PM = (0.70 x 20,000 + 0.78 x 25,000)/(20000 + 25000)
= (14,000 + 19,500)/45000
= 33,500/45000 = $ 0.7444
Question no. 2
The average price of a cotton mixing is $ 0.76/-. The price of component A with a wt.
of 25000 kg is $ 0.79/-. What should be the wt. of component B with a price of Rs.74?
Solution:
PM = (CA + CB)/(WA + WB)
= (PA × WA + PB × WB)/(WA + WB)
0.76 = (0.79 × 25000 +0. 74 × WB)/(25000 + WB)
0.76 (25,000 + WB) = 0.79 × 25,000 +0.74 × WB
19,000 + 0.76 WB = 19,750 +0.74 WB
0.76 WB – 0.74 WB = 19,750 – 19,000
0.02 WB = 750
WB = 37,500 kg
Question no. 3
In a mixing of 3 grades (A, B & C)of cotton, the quantity and price is given below:
Components Weight in kgs Price/kg
A 20,000 80
B 18,000 78
C 16,000 75
Calculate the average price of cotton mixing.
Solution:
PM = (CA +CB + CC)/ (WA + WB + WC)
= (PA × WA + PB × WB + PC × WC)/ (WA + WB + WC)
PM = (80 × 20,000 + 18,000 × 78 + 16,000 × 75)
(20,000+ 18,000+ 16,000)
PM = 4048000
54000
PM = 74.96 Cent/kg
Question no. 4
A cotton mixing consists of 3 grades, the average price of which is $ 0.73/kg. The
quantity and price are bellowed:
Components Weight in kg Price/kg
A 25000 0.78
B 20000 0.73
C ? 0.72
Calculate the wt. of the component C.
Solution:
PM = (CA +CB + CC)
(WA + WB + WC)
= (PA × WA + PB × WB + PC × WC )
(WA + WB + WC)
0.75 = 0.78 × 25000 + 0.73 × 20000 + 0.72 × WC
25000+20000+WC
0.75 (25000+20000+WC) = 0.78 × 25000 + 0.73 × 20000 + 0.72 × WC
WC = 461666.66 kg
Quantity Wise Mixing Ratio of Even Number Component
In order to produce a blend at a pre-determined price a number of components of
different price and quality may be mixed, the method of calculating the
amount of each component in the blend is given below:
Question no. 5
Find out the ratio of 2 components of a cotton mixing to price it at the rate of Cent 75/kg
when component A is purchased at the rate of Cent 73/kg while component B at the
rate of Cent 78/kg.
Solution:
73 (A) 3
78 (B) 2
3+2=5
Ratio = 3: 2
%age of A = 3/5 ×100 = 60 %
%age of B = 2/5 × 100 = 40 %
Verification:
3 kg @ 73 = 219
2 kg @ 78 = 156
5 kg @ 75 = 375
Average price = 375 = 75
Question no. 6
Find out the ratio of 2 components of a cotton mixing, the average price of which should
be Rs.2200/maund and the grade A is purchased @ Rs. 2250/maund while the price of
grade B is Rs. 2125/maund.
Solution:
2250 (A) 75
2200
2125 (B) 50
125
5
Ratio = 75: 50
%age of A = 75/125 ×100 =60%
%age of B = 50/125× 100 = 40%
Question no. 7
There are 4 components in cotton mixing, the average price of which is
Rs.2600/maund. The price of the components is as follows:
A Rs 2800/maund
B Rs 2700/maund
C Rs 2500/maund
D Rs 2300/maund
Calculate the ratio and %age of all components of the given mixing.
Solution:
2800 (A) 300
2700 (B) 100
2500 (C) 100
2300 (D) 200
`=700
%age of A = 300/700 ×100 = 42.85 %
%age of B = 100/700 × 100 = 14.28 %
%age of C = 100/700 × 100 = 14.28 %
%age of D = 200/700 × 100 = 28.57 %
Principle for Pairing: Average price should fall between such components out of which
one should be more and the other should be less.
Quantity-Wise Mixing Ratio of Odd Number of Component
Question no. 8
The average price of 3 components mixing of cotton is Rs.2300/maund. Price of
individual components are as follows:
A Rs. 2350/maund
B Rs. 2375/maund
C Rs. 2250/maund
Also, calculate the mixing ratio of one lakh kg of cotton.
Solution:
2350 (A) 50
2300 2375 (B) 50
2250 (C) 50+75 = 125
=225
Ratios:
A = 50
B = 50
C = 125
Total = 225
Ratio = 2:2:5 = 9:
%age of A = 50/175 × 100 = 28.57 %,
%age of B = 50/175 × 100 = 28.57 %,
%age of C = 75/175 × 100 = 42.85 %,
Verification:
2kg @ 2350 = 4710
2kg @ 2375 = 4750
5 kg @ 2250 = 11250
Average Price =20700/9
= 2300
Question no. 9
The average price of a 3 components mixing is Rs.75/kg. Price of individual components
is as follows:
A. Cotton @ Rs. 2500/maund (37.324 kg)
B. Polyester @ Rs. 80/kg
C. Viscose @ Rs. 103/kg
Calculate the %age proportion of all components using all options. Also, verify the
results.
Solution:
67 (A) (5+28 )= 33
80 (B) 8
103 (C) 8
total= 49
%age of A = 33/49× 100 = 67.34 %
%age of B = 8/49× 100 = 16.32 %
%age of C = 8/49× 100 = 16.32 %
Verification:
33 kg @ 67 = Rs. 2211
08 kg @ 80 = Rs. 640
08 kg @ 103 = Rs. 824
49 kg @ 75 = Rs. 3675
Average Price = 3675/49 = Rs. 75
