Question
Asked May 5, 2019
371 views

Find two positive numbers whose product is 250 such that the sum of the first and four times the second is a minimum.

Just list the larger of the two numbers as your answer.

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Expert Answer

Step 1

Let the two numbers be a & b

Hence, ab = 250

Hence, b = 250 / a

Step 2

Let z = a + 4b = a + 4 x 250 / a = a + 1000 / a

We have to minimize z. 

Z will be minimum if:

  • dz/da is zero
  • d2z/da2 > 0 
Step 3

Let's differentiate z with respect to a.

Recall the famous rule of differentiation: d(x...

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Tagged in

Math

Calculus

Derivative