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Lat cGr) = 0.02r' 12x + 10O00 denote the cst function of firm when x @ the number of units produad What i the marginal cst? [6 marks] () Cakulate € (200)...

Question

Lat cGr) = 0.02r' 12x + 10O00 denote the cst function of firm when x @ the number of units produad What i the marginal cst? [6 marks] () Cakulate € (200) Cive an economic interpretation of the result:. [8 marks] What Isthe "Pproximate €ost f inctelsing the Pradt uction from 1OD to 101 unibs? Compute the results with actual cast inctense. [6 marks]

Lat cGr) = 0.02r' 12x + 10O00 denote the cst function of firm when x @ the number of units produad What i the marginal cst? [6 marks] () Cakulate € (200) Cive an economic interpretation of the result:. [8 marks] What Isthe "Pproximate €ost f inctelsing the Pradt uction from 1OD to 101 unibs? Compute the results with actual cast inctense. [6 marks]



Answers

Find the marginal cost for producing units. (The cost is measured in dollars.) $$ C=4500+1.47 x $$

Mhm The question says marginal cost. The total weekly cost in dollars incurred by link alone records and pressing x component disks. Cf XD function governess. 2000 plus two weeks minus 0.1 X square. Where X growth from zero 26 1000. Now in the party we have to find what is the actual cost incurred in producing the 1001 Desk and 2001 RST Disc. So now in part we we have to find what is the marginal cost when X is equal to 2000 and 2000. Now moving towards the solution here for the given function ceo of X. Now moving towards party for 1001 and stay disk. See of 1001 minus c of 1000 Will be quite to 2000 plus two and 2, -0.001 and two. 1001 sq minus 2000 Plus two and 2000 -0.001 into 1000 square. So solving this equation you will get 1.80 is your answer. Now we have to find when 2001 Discarded. Used. So c. 2001. -C 2000 Will be 2000 Plus two and 2. 2001 0 one into 2001 sq 2000 plus two and 2. minus 0.1 and 2. 2000 square screwing this. To be read your answer as 1.60 Now moving towards part B where let's find the marginal cost that is given by D. C by D. S. So D. C by the X will be equal opportunity by the X. Of 2000 plus two inch works minus 0.1 X square. So it will be equal to zero plus two in two. D by D X of X minus 0.0001 in today by the year Carfax A Square That is to -0.0002 next. So when we bought x equals 2000. And then yeah, busy by dx D. C. by the X will be equal to 1.80. And when access 2000, then Serie dash had 2000 will be called 1.6. Thank you.

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.

We're going to consider the following cost function um which is cmax equals six X. Squared. That's 14 plus 18. And then we also know that this is in thousands of dollars. We want to find the marginal cost That production that will actually cause five. So the marginal cost When we take the derivative so see prime of acts. This is going to be 12 ax plus 14. And then we want to evaluate it at five. So when we evaluate this at five we kept getting 74 And that's gonna be in thousands of $74,000 per unit. Then we want to estimate the cost of raising the production level from 5 to 5.25. So if you look at sea prime of 5.25 Because to 77 Or if we look at sea .5-5 for example, we end up getting this value here. So this is how we can analyze the problem.

All right. So being a CFO is not an easy job you're thinking well what if I could change our marginal profit function from Mp 12 mp two? Would that make us more money if we were able to increase our production from 6 to 8 units? So what you want to know is does your profit go up if you change from Mp 12 Mp two? So what we should do, let's integrate from six units to eight units. And let's assume that mp two of X is bigger than mp one of X. Because if it's not then we don't really care. Right? So here's our integral we're gonna have integral of Mp two fx which is negative one third X cubed plus six X squared minus 20 X. And the integral of M. P. One which is negative one third X cubed plus seven X squared minus 24 X. And we're going to integrate that from 6 to 8. So negative one third X plus negative or minus negative one third X goes away. Six X squared minus seven X squared is negative X squared negative 20 X plus 24 X is for X for integrating from 6 to 8. So we get negative 64 plus 32 minus negative 36 plus 24. So when we put all that together we get negative 32 minus negative 12 or negative 20. Now in this case what that means is negative 20 were saying I think this is going to be more value than this but we end up losing money. So if you have a negative marginal profit it means you're losing money. If you make that choice to switch marginal profit. So I would say do not switch, you'll lose money.


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