find 2 positive numbers whose product is a maximum and whose sum of the first number and four times the second number equals 200
Let the numbers be x and y
x+4y = 200
Product of the numbers = (200-4y)*y =200y-4y^2
This is maximum when the derivative is zero and second derivative is negative
Second derivative =-8 <0
Answer : x=100, y=25
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