1.

Divide a number 1000 in two parts such thatthere product is maximum.

Answer»

Let the two numbers be x and y

so, x+y = 100. => y = 1000-x

now for product to be maximum xy should be maximum or x(1000-x) should be maximum

so, its differentiation should be 0

=> d(x²-1000x)/dx = 0=> 2x -1000 = 0=> x = 1000/2 = 500

so numbers are 500 and 500



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