Q. 125.0( 1 Vote )

A firm has to tra

Answer :

Let the firm has x number of large vans and y number of small vans. We make the following table from the given data:



Thus according to the table, the cost becomes, Z=400x+200y


Now, we have to minimize the cost, i.e., minimize Z=400x+200y


The constraints so obtained, i.e., subject to the constraints,


200x+80y≥ 1200


Now will divide throughout by 40, we get


5x+2y≥ 30…………..(i)


And 400x+200y≤3000


Now will divide throughout by 200, we get


2x+y≤ 15…………..(ii)


Also given the number of large vans cannot exceed the number of small vans


x≤ y……………..(iii)


And x≥0, y≥0 [non-negative constraint]


So, minimize cost we have to minimize Z=400x+200y subject to


5x+2y≥ 30


2x+y≤ 15


x≤ y


x≥0, y≥0


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