Consider the following cost functions.
c. Interpret the ...

Question

Consider the following cost functions.

c. Interpret the values obtained in part (b).

C(x) = 1000+0.1x, 0≤x≤5000, a=2000

Accepted Answer

Below there, today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given the cost function, C of Q is equal to 500 plus 0.05Q for 0 is less than or equal to Q and Q is less than or equal to 10,000, calculate the average cost and the marginal cost at Q equals 4000. Awesome. So it appears for this particular problem, we're asked to solve for two separate answers. We're asked to figure out the average cost, which is our first answer, and the marginal cost, which is our second answer, when Q is equal to 4000 for both cases. So with that said, let's read off our multiple choice answers to see what our final answer pair might be, noting that we'll have our average cost first. And then our marginal cost second. So A is 0.175 and 0.05. B is 0.15 and 0.05. C is 0.175 and 0.1. And finally, D is 0.15 and 0.1. Awesome. So, first off, let us calculate the average cost, and let's denote this as AC. So we'll call this AC, the average cost, and we're trying to calculate the average cost at Q equals 4000. Awesome. So now, in order to do that, we must figure out we need to define the known variables and the target variable we're trying to solve for. So let us know that we're told that CFQ, our cost function, is going to be equal to 500 plus 0.05Q. And let us know that the quantity Q is equal to, once again, 4000, fantastic. And our target variable that we're trying to solve for ultimately is AC, the average cost. So now, in order to do that, we must recall and use the equation to help us solve for the average cost. So let us know that AC, the average cost is going to be equal to C of Q divided by Q. Awesome. So that means that in order to solve for this, we need to substitute in the giving cost and the quantity into our cost formula. So we need to take A C is equal to. 500 plus 0.05 multiplied by our value of Q, which Q is equal to 4000, all divided by our value of Q, which is also 4000. So that will mean that A of C. It's going to be equal to 0.175, and that is our first answer. Hooray, we did it. So now we can solve for our second answer. So now we're trying to figure out the marginal cost, which we'll call this MC, and in order to find MC and once again we're trying to find the marginal cost at Q equals 4000, so using a similar methodology like we did above to solve for our average cost. We need to recall and use the formula to help us solve for the marginal cost, and as we should recall, the marginal cost formula states that MC, the marginal cost is equal to D multiplied by C of Q divided by D multiplied by Q. Where D in this case, Is so D by DQ, so that is our derivative. So we need to differentiate the cost of. So I said it was D multiplied by Q, but it's technically DQ. So D by DQ. So we're differentiating the cost function, so we can state that MC is going to be equal to D by DQ D by DQ is just a fancy way of saying we're differentiating with respect to Q. So MC is equal to D by DQ of. Plugging in our cost equation, which is 500 plus 0.05Q, which when we perform that differentiation, we will find that it's equal to simply 0.05. So that means when we evaluate the derivative, that will mean that MC, our marginal cost will be equal to 0.05, and that is our second and final answer. Hooray, we did it. So therefore, without a doubt, our final answer has to be multiple choice answer letter A, which once again is the average cost is 0.175, and our marginal cost is 0.05. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Consider the following cost functions.
c. Interpret the values obtained in part (b).
C(x) = 1000+0.1x, 0≤x≤5000, a=2000

Key Concepts

Cost Function

Interpretation of Values

Constraints on Production

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