Q11 A farmer is engaged in breeding pigs. The pigs are fed on various products grown on the farm. Because of the need to ensure nutrient constituents, it is necessary to buy additional one or two products, which we shall call A and B. The nutrient constituents (vitamins and protein) in each of the product are given below:
Q11 A farmer is engaged in breeding pigs. The pigs are fed on various products grown on the farm. Because of the need to ensure nutrient constituents, it is necessary to buy additional one or two products, which we shall call A and B. The nutrient constituents (vitamins and protein) in each of the product are given below:
Nutrient Constituents
Nutrient in the product
Minimum requirement of nutrient constituents
X
36
6
108
Y
3
12
36
Z
20
10
100
Product A costs Rs. 20 per unit and Product B cost Rs. 40 per unit Determine how much of products A and B must be Purchased so as to provide the pigs nutrients not less tan the minimum required, at the lowest possible cost. Solve graphically.
Ans: Minimize (Z) = 20×1+40×2 Subject to constraints 36×1+6×2≥108, 3×1+12×2≥36, 20×1+10×2≥100 Non Negative Restrictions x1, x2≥0
Z=160 x1=4, x2=2
