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Cost analysis: company with two cifferent plants manufactures guitars and banjos. Its production costs for each instrument ORI are given in thc following matrices. ...

Question

Cost analysis: company with two cifferent plants manufactures guitars and banjos. Its production costs for each instrument ORI are given in thc following matrices. Chocd Plant X Flant foor Guitar Banjo Guitar Banjo Materials 351 337 580 543 ]appe Hosan Labor 581 5102 8101 5137Find 7(A + B), the average cost ol production for the two plants Lifat d provil Wu sly {0 fce 5(+8) =(Type integers decimals ) cutol Henaumned Jional ngl

Cost analysis: company with two cifferent plants manufactures guitars and banjos. Its production costs for each instrument ORI are given in thc following matrices. Chocd Plant X Flant foor Guitar Banjo Guitar Banjo Materials 351 337 580 543 ]appe Hosan Labor 581 5102 8101 5137 Find 7(A + B), the average cost ol production for the two plants Lifat d provil Wu sly {0 fce 5(+8) = (Type integers decimals ) cutol Henaumned Jional ngl



Answers

A company with two different plants manufactures guitars and banjos. Its production costs for each instrument are given in the following matrices: (FIGURE CAN NOT COPY) Find $\frac{1}{2}(A+B),$ the average cost of production for the two plants.

So here we have have been given a Matics A, which indicates the production levels off three factories producing accosting adults on electric adults in the Magic is 70 50 25 to fight 100. So so now you have to understand the first. This is the production level off the first factory on this is the production level off the second factory, and this is the production level off the third fact and horizontally. This is the production level off acoustic guitars, and this is the production level Off electric. Now the first question asks us to calculate the Element eight toe. Now the Element eight or two is the element in the second role on board. Second, call it off. Romantics. Hey, now we have to search for second row and second column element. Now this'll is the second. Andi This'll is the second column, so the element, which is in the second roll on in the second column, is 100. Therefore, the element A two is equal to 100 so they are done in the first part of the push. Let's move to the second part of the question, which asks us to calculate it. Asked spoke calculate the production levels when increased by 20% way help mechanically in the production, millions off each off each factory when there increased by 20 people. Well, let's say, for example, there is a There is a come. There is a factory which produces a production level off hundreds. Andi, if it is increased by 20% then go find a new production level. We simply multiply 101 20% which is we might play 100 by 1.2. The answer is 1 20. So similarly, in this multi Magnetics we have to multiply each production level by one by two. And for this we will make you so scale of multiplication. It is well, multiply this and they're Matics by one point. And we know that in scaler multiplication we help the multi play each element off the metrics. Violence Caleb way have will multiply 1.2 but each element the mathematics he and therefore we will get the production level metrics after an engraver 20% and that is equal to 84. 16. The seats 42 1, 20 and 84. So this is the production level. Metrics off the train factories off an increase off 20%. So we are even completed the top on the now let's move to the party in part C. It has been mentioned that from Al costume you could talk. The sale on the cost is $80 and put electric guitar. It means 1 $20 and we are asked to find that total. See? Yeah, and we are asked to find the total sales value off Peters. So for this, what will lose be Contra Matic See which contains the cost this 80 and one and he beheld of Matics eight, which is the protection level. Matics 70 50 when he fights and 3500 seven now to find the total sales for each factory way have to simply multiply thes two mattresses, that is, we have to multiply the mattresses c on it because that when you watch the total things for each fact, so this Matics multiplication it's possible because dramatic c is off the order one by two Mathematics Azov The order toe by three The number off columns automatic C is equal to the number off clothes off dramatics. But we know how my application off my face is Eastern. We select intelligent in each off the force Matics and we multiplied the corresponding elements off each column off the second man picks and then adding the simple isn't it? So you multiply 80 and 70 which is the cost off. A coasting results for the first factory plans 1 2035 which is the total sale off electric vehicles from the first country. First factor similarly, for the second factory is 80. My deployed by 50 glass, one continual deployed about 100 and finally, for the perfect third one, it is 18 multi plane by 25 plus 1 20 multiplied by seven mhm. The final result tent off Matic. See, it will be 9000 800 16 ozone and 10,400. So this is the total sales are dinner the proton sales for each factories and then we'll learn the party as well

We're told that a music company estimates that the marginal cost of producing its professional series guitars is C. Prime of X equals point 00 two X plus 100 dollars per month. When the level of production is X guitars per month, we're told that the fixed costs incurred this one. Yes. Yeah, that's a long. Yeah, Our $4,000 per month. We're asked to find the total monthly cost incurred by Carlotta and manufacturing X guitars per month well defined totally monthly cost. We want to integrate our marginal cost for the month. So this is the anti derivative of C. Prime of X. This is the anti derivative of .002 x plus 100 with respect to X. Which is equal to 0.1 X squared plus 100 X plus some constant that I'll call a lobster. That's true. Now to find the value of a notice that our fixed costs exists no matter the level of manufacturing for the guitars. So even if you produce zero guitars, we still have fixed costs of $4,000 per month. So we have 4000 is equal to see of zero, which is 0.1 times zero squared plus 100 times zero plus A, which is just a. So a. is equal to 4000. and therefore it follows that the total monthly cost in manufacturing X guitars per month is C. F X equals 0.1 X squared Plus 100 x plus 4000, and this is in dollars.

Yes, for this problem, we are told that Carlotta Music Company estimates that the marginal cost of manufacturing, it's professional series guitars, you see prime of X equals 0.2 X plus $100 per month. When the level of production is X guitars per month. We're also told that the fixed costs incurred by Carlotta are $4,000 per month. You're then asked to find the total monthly cost incurred by Carlotta and manufacturing X guitars for a month. So what we have to do here is find the anti derivative of C prime of X there. So we know that cfX is going to be 0.1 X squared from um, the anti derivative of X going to X squared over two, Then the anti derivative of 100 is going to be 100 x. And then we would have a constant. But contextually we're told the fixed costs are $4,000 per month, so the constant of integration is just going to be 4000.

You guys leads to problem 34. In this problem, we need to find the exact post and the approximate cost of producing 51st gator. The total cost of producing um X readers is given here is the cost function To find the exact cost. What we need to do is we need to find the total cost of producing 51 guitars and we need to find the total cost of producing 50 m. When we get these two amounts, say we get X and why as the total M. O. We need to subtract why the total cost of producing 50 m from the total cost of producing 51 m. And we will get them the cost of producing 51st gator. It's true that The total cost of producing 51 gator can be found by substituting eggs as 51 in discussed function equation. Let's do that. The cost will be then 1000 plus 100 multiplied by X, which is 51,- 0.25 multiplied way 51 is square. And we get $5,449.75 as the total cost of producing 51 caters. Then we need to find the total cost of producing executive 50 m. Again in the cost function equation here we need to substitute 54 x. Let's do that. Then 1000 plus 100 multiplied by 50 which is X -0.25 multiplied by 50 square. And this calculation gives us $5,375 Next weekend. Find what is the exact cost of producing 51st reader by subtracting The total cost of losing 50 m From the total cost of producing 51 m. and we are subtracting 5375 from 5449.75. When we do this obstruction, we get the exact cost of producing 51st leaders as $74.75. The next problem says us to calculate the approximate cost of producing the 51st guitar. What we need to do is we can calculate the cost of producing 51st electric heater By approximation. When we compute the marginal cost function at X is equal to 50. And we know that when we take the first derivative of the cost function, we get the marginal cost function, which we do notice. See primex and the cost function is given. We need to differentiate it with respect to X. Let's do this. This differentiation. 1000 is a constant. When we differentiated we get zero, then we have 100 X. When we differentiate 100 X. We get 100. Because 100 years are constant and we are differentiating only eggs. And when we differentiate X. With respect to X. We get one And one multiplied 100 gives us 100. Then we have this negative sign. It will remain here. And Then we are differentiating excess square because their .25 is a constant. It will come out and we will differentiate x square. When we differentiate Texas where we get 26. And when we multiplied 0.25 by two A six we get 0.5. And we get the marginal cost function as 100 miners 0.5 X. And at executing 50. The marginal cost function is 100 -0.5. multiplied, weigh 50 Which gives us 75. Therefore the approximate cost of perusing 51st guitar is $1.75. Therefore we have this exact value which is $74.75. And the approximate cost is dollar seven.


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