Question
2: A paint manufacturing organization produces two
qualities of paint – Premium paint and Economy paint. It requires three main
chemicals for their production – Chemical A, Chemical B and Chemical C. One
litre of Premium paint requires 150 units, 250 units and 200 units of Chemical
A, Chemical B and Chemical C respectively. Similarly, one litre of Economy
paint requires 200 units and 100 units of Chemical A and Chemical B
respectively. Manufacturing process of Economy paint gives 50 units of Chemical
C per litre of paint production as by-product.
Chemical A, Chemical B and Chemical C are available per
day in 3000 units, 5000 units and 1000 units respectively. Premium paint gives
a profit of 300 Rs./litre whereas Economy paint has a profit of Rs. 200 /litre.
a) Formulate a linear program to maximize the profit by
producing the two types of paints. (4 marks)
b) Use Graphical Method to recommend the optimum product
mix. (Draw it on the normal answer sheet showing scale of the two axes.
Approximate drawing and answer will be fine if the answer is logically
correct). (6
marks)
c) Suppose these
Chemicals are hazardous, and they should be used entirely on daily basis. You
can reduce the availability of these chemicals to meet this condition. Availability
of which chemicals would you reduce and by how much? (10 marks)Answer is available in a video at https://drive.google.com/file/d/1o2Q80IvsB1NbR_imSy77APbFZrmU6kY2/view?usp=sharing
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