# A company produces soft drinks that has a contract which requires that a minimum of 80 units of the chemical

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A company produces soft drinks that has a contract which requires that a minimum of 80 units of the chemical A and 60 units of the chemical B go into each bottle of the drink. The chemicals are available in prepared mix packets from two different suppliers. Supplier S had a packet of mix of 4 units of A and 2 units of B that costs  10. The supplier T  has a packet of mix of 1 unit of A and 1 unit of B that costs ₹4. How many packets of mixes from S and T should the company purchase to honour the contract requirement and yet maintain the minimum cost ? Make a LPP and solve graphically.

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Let x and y units of packet of mixes are purchased from S and T respectively. if Z is the total cost, then

Z = 10x+4y       ....(i)

is objective function which we have to minimize Here constraints are

4x+y ≥ 80   ...(ii)

2x+y ≥ 60   ...(iii)

x ≥ 0               ..(iv)

y ≥ 0            ....(v)

On plotting the graph o{ above constraints or inequalities (ii), (iii), (iv) and (v), we get shaded region having corner point A, P, B as feasible region.

For co-ordinate of P  Since the graph of inequality (viii) does not have any point common.

So the minimum value of Z is 260 at (10,40). i.e., minimum cost of each bottle is 260 if the company purchases 10 packets of mixes from S and 40 packets of mixes from supplier T.

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