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1ccO Given that C(x) = 5000+ 10Ox is the totab cost indollars of producing x machinesdetermine the exact cost of producing the 1Ith machine.Select one: S195.31b. S5...

Question

1ccO Given that C(x) = 5000+ 10Ox is the totab cost indollars of producing x machinesdetermine the exact cost of producing the 1Ith machine.Select one: S195.31b. S5109.09S109.09d. S5004.69

1ccO Given that C(x) = 5000+ 10Ox is the totab cost in dollars of producing x machines determine the exact cost of producing the 1Ith machine. Select one: S195.31 b. S5109.09 S109.09 d. S5004.69



Answers

The total cost (in dollars) of producing $x$ food processors is $C(x)=2,000+50 x-0.5 x^{2}$ (A) Find the exact cost of producing the 21 st food processor. (B) Use marginal cost to approximate the cost of producing the 21 st food processor.

The following problem were given a cost function. c. vax equals 2000. That's the fixed cost. And then we have variable cost 100 x -0.1 x Squared. I want to find the average cost of producing 100 washing machines Subcommittee c. of 100 11,000. And we want to find the marginal cost 100 machines are produced that's going to see prime of 100 and that's 80. So when the marginal costs um as at 100 washing machines, we want to show The cost of producing one more um after it's been initially given. So if we have 100 1, for example, about the same price which it is getting cheaper as we continue, so that's going to be the marginal cost declining.

For this problem. We're being given this formula that approximates the total cost when producing washing machines part A assets approximate that average cost per wash machine when we make 100. So basically, we just take the formula for this 400 machines into, like 100 right? Because this is essentially the formal, um, estimated cost for Exeter missions. Right. And we can plug in our values 1000 plus squared minus 0.1 times squared. I'm good for the top value. Released. What? It was 10 times under the right. So they get minus 1000 over 100 right? We could take out two zeros from police 20 minus 10 plus 100. Um, which gives us the average cost per machine would be 100 $10. Okay, so the under part B is asking was the marginal cost at $100? So to find a marginal cost, we can essentially just take the driven dio great d c. Ever since p x, um of thes equation that we have here, right? And we take the derivative we get that this value becomes 100 minus 0.2 x and ah x equal. It's 100 because we have 100 washing machines produced. This comes 100 Nice 20 and are marginal. Cost is $80 Really under part C. Exhausting has to show that if we were Teoh produced 101 machines, right, that the marginal that the difference between this and 100 machines would equal the marginal cost. Right. So it's true this, um we can essentially do that exactly and write another form of marginal costs because marginal costs is the slope of, uh, this equation. Essentially, we know that slope is rise over run, right. So change and see over change in X, and we can plug in the values of C 401 and 100. So by doing so, we get that this marginal cost could be estimated like so And then we confined our values of C 101 right. This becomes 2000 plus 100 times 101 one of those 10.1 times 101 squared, see, of 100 equals 2000 posts 100 times 100 minus point born times 100 squared. So because is this attracting this from that Well in fact we could. It's a little messy. Who can subtract two of these cramp slow, right if you subtract this from this weekend 100 right 100 minus 20 0.1 In this. Basically, Kissel's $79.90 has the answer. So the difference between the making 100 1 and making 100 washing machines and this is approximating similar to our martial calls. It's very similar to a, and you can find this values are all using a calculator, yes.

So for this problem we have a cost function. It is 1000 plus five X plus 0.1 X. Squared. Um And there's no restriction really on the domain other than the fact that Um you can either sell zero mountain bikes or you can sell um as many more than that. So we'll have X. Being greater than Or equal to zero. Then we want to sketch the graphs of average cost and marginal cost. So average cost is going to be um this graph right here we take this graph. The marginal cost is fairly easy because it's just the derivative of the cost function. And the average cost function is going to be um this one right here except it'll be G of X. I won't have it looking like this. We see that this right here is the average cost function and we see that the minimum average cost will be located right here approximately. Excellent. Um It's actually going to be the minimum average cost in this case Is going to be 0 um or approximately right there. We take jeep prime of acts and look more specifically, We see that the minimum average cost is at x equals 100.

So we have this cost function C. And we're going to find the marginal cost function M. Which is equal to see prime or the first derivative of our cost function. And so we can say M is equal to the derivative of 205,000 plus 9800 times X. And what we can do first is we can split this derivative up, since if we have the derivative of one term plus another term is equal to the derivative of the first term, plus the derivative of the second term. And now this first term is just a constant. And we know that the derivative of constance is just equal to zero. So we really just need to deal with this derivative of 9800 times X. And what we can do is we can take out the 9800 since it's a constant and multiply it by the derivative of X. And now we just have 9800 times the derivative of X. And we can use the power rule to find the derivative of X here and is equal to one where we have X to the first, so we bring down the one times it by X to the one minus one power, or X to the zero power, which is just one. So are a derivative is equal to 9800. Therefore our marginal cost function is just equal to 9800.


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