If C(x) is the cost of producing x units of a commodity,...

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 3,000 + 210x + 6x^3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 402736.7 (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 402.7 per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ 494.6 per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) 10.1 units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ 5313 per unit

Transcript

00:01 Hi there, so for this problem, we are told that the cost function that we are given for this, c of adds, is equal to 3 ,000, and then this plus 210 times adds, and then this plus six times adds to the 3 divided by 2.

00:26 Now, for the first question, for part a of this problem, we are asked about to find a total cost at a production level of 1 ,000 units.

00:37 So what we need to do is to evaluate the expression that we are given at 1 ,000.

00:42 So that will be then 3 ,000 plus 210 times 1 ,000.

00:49 And then this plus 6 times 1 ,000, elevated to 3 ,000.

00:56 Divided by 2.

00:58 Then let's use our calculator to see what value we obtained for this.

01:11 Okay, then the value that we obtained for this is we need to give this to the nearest cent.

01:22 So that will be then.

01:24 40 ,000.

01:27 Oh no, it's 402, 402, 737736.

01:38 066.

01:43 Remember, you need to answer this to the nearest cent.

01:50 Now we keep going.

01:52 For part b of this problem, the question is to find the average cost at a production level of 1 ,000.

02:02 Now, again, first of all, remember that the average cost is just the cost function divided by x.

02:09 So that will be then 3 ,000 divided by ads, then this plus 210 plus 6, and then we will have x elevated to 1 divided by 2, if i'm correct, because 3 divided by 2 minus 1 is 0 .5, sorry.

02:32 So now we just need to evaluate this at 1 ,000.

02:35 So let's do that.

02:39 This plus 210 plus 6 times 1 ,000 elevated to 1 divided by 2.

02:50 So let's see what value we obtained from our calculator.

02:54 Again, i think it is to the nearest cent.

03:02 Again, we need to include two decimal places.

03:08 Okay, let me see, let me use the calculator.

03:13 And the value that we obtained for this is 400.

03:17 0 .72 .74.

03:26 So that's a solution for part b of this problem...

Question

Please give Ace some feedback