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CBSE Class 12-science Answered

A factory produces two compounds P and Q. The following table gives the units of ingredients A and B (per unit) of compounds P and Q and also minimum requirement of P and Q. Cost per unit of P and Q are also given:   Compound per unit Minimum Ingredient P Q Requirement C (per unit) D (per unit) 1 3 2 1 80 75 Cost per unit (in Rs) 4 6   Find the quantities of P and Q which would minimize the cost.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Let x units of P and y units of Q be produced we have the following LPP
          Minimise z = 4x + 6y
          st x + 2y  80
          3x + y  75
          x  0, y 0
         

Corner Points

Z = 4x + 6y

A(80, 0)
B(14, 33)
C(0, 75)

z = 320
z = 254
z = 450

Z is minimum at B(14, 33)
Hence, the cost is minimum when 14 units of P and 33 units of Q are produced and minimum cost is Rs 254.

Answered by | 04 Jun, 2014, 03:23: PM

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