Q. 295.0( 1 Vote )

A company produce

Answer :

Let “a” be the number of units of product 1 produced in one day and b be the number of units of product 2 produced in one day


The selling price of product 1 is 9rs and cost price is 1.2rs hence a profit of 9 – 1.2 = 7.8rs. Profit behind ‘a’ product will be 7.8a


The selling price of product 2 is 8rs and cost price is 0.9rs hence a profit of 8 – 0.9 = 7.1rs. Profit behind ‘b’ products will be 7.1b


Hence total profit daily z = 7.8a + 7.1b


We have to maximize this profit ‘z = 7.8a + 7.1b’ based on some constraints


Let us identify the constraints now


Constraint1: Assembly work


Product 1 requires 1/4 of an hour of assembly work per unit hence for ‘a’ units of an hour of time will be required


Product 2 requires of an hour of assembly work per unit hence for ‘b’ units of an hour of time will be required


Number of hours available for assembly work is 90


Hence the total time of assembly work for product 1 and product 2 should not be greater than 90



Multiply by 12


3a + 4b ≤ 1080 …(i)


Constraint2: Quality control work


Product 1 requires of an hour of quality control work per unit hence for ‘a’ units of an hour of time will be required


Product 2 requires of an hour of quality control work per unit hence for ‘b’ units of an hour of time will be required


Number of hours available for quality control work is 80


Hence the total time of quality control work for product 1 and product 2 should not be greater than 80



Multiply by 24


3a + 8b ≤ 1920 …(ii)


Constraint3: The maximum amount of sale of product 1 daily is 200 units.


a ≤ 200 …(iii)


Also, as “a” and “b” represent number of units produced hence it cannot be negative hence a ≥ 0 and b ≥ 0


Plot equations (i), (ii) and (iii) and mark their intersection points


Now in (i) and (ii) less than means below the lines and in (iii) a < 200 means to the left of a = 200


Take scale


On X-axis 1cm = 50 units


On Y-axis 1 cm = 50 units



Now the corner points are F, D, E, G and O


Let us find values of z at these points



Hence the maximum value of z is 2412 at E (200, 120)


Hence the maximum profit is Rs 2412.


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