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CBSE Class 12-science Answered

  A diet is to contain atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of calcium. Two foods f1 and f2 are available. A unit of food f1 contains 1 unit of vitamin A, 2 units of vitamin B and 3 units of calcium and a unit of food f2 contains 2 units of vitamin A, 2 units of vitamin B and 1 unit of calcium. If one unit of food f1 costs Rs 16 and one unit of food f2 costs Rs 20, find the least cost of the mixture which will produce the desired diet.
Asked by Topperlearning User | 29 Jul, 2016, 10:09: PM
answered-by-expert Expert Answer

 

Problem can be represented as
          Minimise z = 16x + 20y
          st x + 2y  10
          2x + 2y  12 or x + y  16
          3x + y  8
          x  0, y  0
         

Corner Points

Z = 16x + 20y

A(10, 0)
B(2, 4)
C(1, 5)
D(0, 8)

Z = 160
z = 32 + 80 = 112
z = 16 + 100 = 116
z = 0 + 160 = 160

 Since the lowest cost in the second column is Rs.112, the minimum cost occurs at B(2,4)

Thus, the desired diet consists of 2 units of food 1 and 4 units of food 2.

Answered by | 30 Jul, 2016, 12:09: AM

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