Q18 of 97 Page 1376

A company producing soft drinks has a contrast which requires a minimum of 80 units of chemical A and 60 units of chemical B to go in each bottle of the drink. The chemical are available in a prepared mix from two different suppliers. Supplier X has a mix of 4 units of A and 2 units of B that costs ₹10, and the supplier Y has a mix of 1 unit of A and 1 unit of B that costs ₹4. How many mixes from X and Y should the company purchase to honor the contract requirement and yet minimize the cost?


Let x and y be number of mixes from suppliers X and Y.


∴According to the question,


4x + y , 2x + y


Minimize Z = 10x + 4y


The feasible region determined by 4x + y , 2x + y is given by



The feasible region is unbounded .The corner points of feasible region are A(0,80) , B(10,40) , C(30,0).


The value of Z at corner points are



The minimum value of Z is 260 at point (10,40).


Hence, the company should buy 10 mixes from supplier X and 40 mixes from supplier Y to minimize the cost.


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