A company is producing a new product due to the nature of...

A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x)= 2+0.4 (1/x) where T(x) is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 5 ; units 20 through 25.

Transcript

00:01 In this question, we're given a function that tells us how many hours it takes to produce an x unit of a product.

00:09 And we want to try to find the total amount of time it takes to produce units 1 through 5, and the total amount of time it takes to produce units 20 through 25.

00:19 Now, there are two ways we can go about answering this.

00:22 I'm going to call the first method the approximation method.

00:26 If you've not seen integrals yet, this is probably the best method for you to use.

00:31 So what we're going to do is we're going to use the function that we're given and evaluate it for one unit, two units, three units, all the way to five units, and then add all those times that we get from these functions together.

00:49 So for one unit, it'll take us about 2 .4 hours.

00:53 For two units, it's going to take us about 2 .2 hours.

00:56 And then i'm going to speed it up a little bit.

00:58 For three units, it's going to be about 2 .13 hours.

01:03 2 .1 hours for 4 units and about 2 .08 hours for 5 units.

01:09 So if we add all these times together, we're going to get an approximation for the total amount of time it takes us to make units 1 through 5, which is about 10 .91 hours.

01:21 I'm going to do the exact same thing for units 20 through 25.

01:25 So here i'm just going to put all those solutions on the screen at once...

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