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Dairy

by shashank.ism » Tue Feb 09, 2010 7:13 am
In "Dairy", milk is processed to produce "Pure Ghee" and "SNF". One kg of milk should be processed to produce 5 gms of pure ghee and 80 gms of SNF. Pure Ghee and SNF are sold at Rs.120/kg and Rs.200/kg respectively. If the cost of processing the milk is Rs.6/kg and the fixed cost of running the "Dairy" for a day is Rs.300, then which of the following can be the total quantity (in kgs) of milk processed per day and the corresponding cost (in Rs./kg) of milk such that the "Dairy" makes a profit of 10% per day?

120, 12
120, 10
150, 15
150, 12
150, 10
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by ajith » Tue Feb 09, 2010 12:16 pm
shashank.ism wrote:In "Dairy", milk is processed to produce "Pure Ghee" and "SNF". One kg of milk should be processed to produce 5 gms of pure ghee and 80 gms of SNF. Pure Ghee and SNF are sold at Rs.120/kg and Rs.200/kg respectively. If the cost of processing the milk is Rs.6/kg and the fixed cost of running the "Dairy" for a day is Rs.300, then which of the following can be the total quantity (in kgs) of milk processed per day and the corresponding cost (in Rs./kg) of milk such that the "Dairy" makes a profit of 10% per day?

120, 12
120, 10
150, 15
150, 12
150, 10
Let x => Total Quantity of milk processed (in Kg)
y=> Cost/kg of milk

Now,
1 Kg. of milk gives 50g. of pure ghee and 80 g of SNF

Thus,
x kg of milk gives 50x g of pure ghee and 80x g of SNF

Total Cost = 300 + 6x + xy
Revenue from pure ghee= (50/1000)*120*x = 6x
Revenue from SNF = (80/1000)*200*x = 16x

Thus, Total Revenue = 22x
For 10% profit,

1.1(300 + 6x + xy) = 22x
330 + 1.1xy = 15.4x

=> x = (3300)/(154 - 11y)

For y = 12, x = 150
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by komal » Wed Feb 17, 2010 11:43 am
shashank.ism wrote:In "Dairy", milk is processed to produce "Pure Ghee" and "SNF". One kg of milk should be processed to produce 5 gms of pure ghee and 80 gms of SNF. Pure Ghee and SNF are sold at Rs.120/kg and Rs.200/kg respectively. If the cost of processing the milk is Rs.6/kg and the fixed cost of running the "Dairy" for a day is Rs.300, then which of the following can be the total quantity (in kgs) of milk processed per day and the corresponding cost (in Rs./kg) of milk such that the "Dairy" makes a profit of 10% per day?

120, 12
120, 10
150, 15
150, 12
150, 10
total cost= (k(6+c)+300)(milk processed=k)
sold =1.1x[k(6+c)+300]=(50/1000)xkx120+(80/1000)xkx200
=6k+16k=22k
330=kx[22-1.1(6+c)]=k[22-6.6-1.1C]=k[15.4-1.1C]
when c=12 ,k=150
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