Question

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?

Answer 1

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

∴According to the question, 

4x + y ≥ 80, 2x + y ≥ 60, x ≥ 0, y ≥ 0 

Minimize Z = 10x + 4y 

The feasible region determined by 4x + y ≥ 80, 2x + y ≥ 60, x ≥ 0, y ≥ 0 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

Corner Point	Z = 10x + 4y
A(0, 80)	320
B(10, 40)	260	Maximum
C(30, 0)	300

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.