Question

Asked May 5, 2019

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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.

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
- d
^{2}z/da^{2}> 0

Step 3

Let's differentiate z with respect to a.

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

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