A company manufactures three kinds of calculators : A, B and C in its two factories I and II.

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A company manufactures three kinds of calculators : A, B and C in its two factories I and II. The company has got an order for manufacturing at least 6400 calculators of kind A, 4000 of kind B and 4800 of kind C. The daily output of factory I is of 50 calculators of kind A, 50 calculators of kind B and 30 calculators of kind C. The daily output of factory II is of 40 calculators of kind A,20 of kind B and 40 of kind C. The cost per day to run factory I is Rs. 12000 and of factory II is Rs.15000. How many days do the two factories have to be in operation to produce the order with the minimum cost ? Formulate this problem as an LPP and solve it graphically.

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Let factory (i) run x days and factory (II) run y days. Then,

value of Z is Rs.1860000 attained at the point (80, 60). hence, factory (I) should run for 80 days and factory (II) should run for 60 days to get a minimum cost.