Suppose the cost of producing x lawn mowers is C(x) = −0.02x²+...

Question

Suppose the cost of producing x lawn mowers is C(x) = −0.02x²+400x+5000.

a. Determine the average and marginal costs for x = 3000 lawn mowers.

Accepted Answer

Welcome back, everyone. The total cost in dollars for producing T tablets is given by C of T equals -0.04 T2 plus 600 + 7000. Find the average in marginal costs when T is equal to 2500 tablets. So first of all, let's recall how we calculate the average cost so we can take the average cost C. Of tea And we have to recall that it is going to be equal to C of T, the cost function, divided by T. So essentially this is the formula that we want to use, right? And we can begin solving for it. We want to identify the average cost. At 2500 tablets. So what we want to do is simply take the original function C of T and evaluate it at 2500, so we can replace T with with 2500. So we take C of 2500 and divide that by 2500. So this is the first part. We're going to take our function -0.04, multiply it by T2, so 2500 squad. We are going to add 600 multiplied by 2500. We're going to add 7000, and then we are dividing the result by 2500. So for this part, we're going to get 502.80. We have our average cost. Now, let's identify the marginal cost. Now, for the marginal cost, we have to take the derivative of CFT. So we want to identify the marginal cost function to begin with. And this means that we are differentiating 0.04 T2 plus 600T plus 7000. So let's apply the power rule for the first term we're going to get negative 0.08T because the derivative of T squared is 2T. We're going to add 600 because the derivative of T is 1 and the derivative of a constant is 0. And now let's identify the marginal cost function at 2500. So this means that we're taking 0.08, multiplying that by 2500, and adding 600. When we perform the calculations, we're going to get 400. So now, the average cost Yes 500 And 2 point. $80 for the marginal cost. We got $400 so $400.00. And those will be our final answers to this problem. Thank you for watching.

Suppose the cost of producing x lawn mowers is C(x) = −0.02x²+400x+5000.
a. Determine the average and marginal costs for x = 3000 lawn mowers.

Key Concepts

Cost Function

Average Cost

Marginal Cost

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