A company is considering the purchase of a piece of...

A company is considering the purchase of a piece of equipment to be used to manufacture a new product. Four machines are being considered. The following table summarizes the purchase cost of each machine and the associated variable cost of production if the machine is used to produce the new product. Determine the ranges of output over which each machine would be the least costly alternative. Purchase Cost Variable Cost/Unit Machine 1 $ 80,000 $10.00 Machine 2 120,000 9.00 Machine 3 200,000 7.50 Machine 4 300,000 5.50

Transcript

00:01 All right, so let's write our total cost functions for each machine.

00:05 I have total cost for machine one, which is the purchase cost.

00:10 That's the fixed cost plus the variable cost, which is 10 ,000 times the number of units produced.

00:19 The total cost for machine two is going to be a hundred and twenty thousand plus nine.

00:28 Where did that 10 ,000 come from? that should be just ten.

00:34 Ten dollars times the number of units produced.

00:38 And then for machine two it was a hundred and twenty thousand, which is your fixed cost plus 9x.

00:47 For machine three you have a fixed cost of two hundred thousand and then a variable cost of 7 .5 times the number of units produced.

00:59 And for machine four you have a fixed cost of three hundred thousand and a variable cost of 5 .5 times the number of units produced.

01:13 And we want to know the ranges over which each machine would be least costly alternative.

01:23 Well, let's see how we would do this.

01:37 If tc1 is the least costly, then 8 ,000 plus 10x would be less than a hundred and twenty thousand plus 9x, which means that subtracting 9x from both sides i get x.

02:04 Subtracting 80 ,000 from both sides i get 40 ,000.

02:11 So this is for machine two.

02:17 And then 80 ,000 would also be less than the cost from machine three, so 200 ,000 plus 7 .5x.

02:31 So this was machine three.

02:34 And then subtracting 7 .5x from both sides and 80 ,000 from both sides so that then gives me x is less than 120 ,000 divided by 2 .5.

02:53 That is 48 ,000.

02:57 And it would have to be less than the cost of using machine four, so 300 ,000 plus 5 .5x.

03:12 And that means that 4 .5x has to be less than 220 ,000.

03:21 So x would have to be less than 4 .5.

03:51 Okay, so if x is less than 40 ,000 it is the least expensive because it satisfies all of those.

04:09 Then let's see here.

04:12 Tc2 is least expensive.

04:18 Or machine two...

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