Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values for rice are 0.05 g and .5 g respectively. Wheat costs Rs.4 per kg and rice Rs.6 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 5 g and 200 g respectively. In what qualities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of protiens and carbohydrates at minimum cost. Form a L.P.P and solve it graphically.
Answers
Hence having only Rice in the daily diet provide minimum daily requirements of protiens and carbohydrates at minimum cost
in another asumption 40 gram of Wheat & 20 gram of Rice
Step-by-step explanation:
Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates.
The corresponding values for rice are 0.05 g and .5 g respectively
W gram of Wheat & R gram of Rice
Then Protein = 0.1W + 0.05R ≥ 5
=> 10W + 5R ≥ 50
=> 2W + R ≥ 100
0.25W + 0.5R ≥ 200
=> W + 2R ≥ 800
4W/1000 + 6R/1000 should be minimum
2W + 3R should be minimum
W R 2W+R
800 0 1600
700 50 1550
600 100 1500
500 150 1450
400 200 1400
300 250 1350
200 300 1300
100 350 1250
0 400 1200
Hence having only Rice in the daily diet provide minimum daily requirements of protiens and carbohydrates at minimum cost
If carbohydrate is 20 gram instead of 200
2W + R ≥ 100
W + 2R ≥ 80
2W + 3R should be minimum
W R 2W + 3R
50 15 145
40 20 140
30 40 180
W = 40 & R = 20 will give minimum cost
40 gram of Wheat & 20 gram of Rice
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