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PART BA bicycle factory makes two models, five-speeds and ten-speeds Each week, the total cost (in dollars) to make five-speeds and ten-speeds is C(xy)=1O.000+50x+ ...

Question

PART BA bicycle factory makes two models, five-speeds and ten-speeds Each week, the total cost (in dollars) to make five-speeds and ten-speeds is C(xy)=1O.000+50x+ 70y-0.Sxy.The production manager wishes to make between 100 and 150 five-speeds and between 80 and 120 ten-speeds. What combination will cost the most?

PART B A bicycle factory makes two models, five-speeds and ten-speeds Each week, the total cost (in dollars) to make five-speeds and ten-speeds is C(xy)=1O.000+50x+ 70y-0.Sxy.The production manager wishes to make between 100 and 150 five-speeds and between 80 and 120 ten-speeds. What combination will cost the most?



Answers

A manufacturer produces two models of mountain bicycles. The times (in hours) required for assembling and painting each model are given in the following table: $$ \begin{array}{|c|c|c|}\hline & {\text { ModelA }} & {\text { Model B }} \\ \hline \text { Assembling } & {5} & {4} \\ \hline \text { Painting } & {2} & {3} \\ \hline\end{array} $$ The maximum total weekly hours available in the assembly department and the paint department are 200 hours and 108 hours, respectively. The profits per unit are $\$ 25$ for model $A$ and $\$ 15$ for model B. How many of each type should be produced to maximize profit?

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So here was a problem that could be solved by reducing a matrix. So a production company has two miles of bicycle. I have a model to a one and the model 301 The model to a one takes your car company two hours to build. They cost $18 to make about 301 takes three hours, three hours to build and 27 dollars to make unless his company has daily production budget of 34 hours and $335. Okay, now. But not question to ask is how many of and pure one bikes and and 301 bikes do we need to manufacture so that we used up Oh, are allotted time and money. So first things first, we consider the time we have 34 hours to burn in the day, so therefore it's two hours per m. Two a one bike plus three hours per m, +301 bike and that at the 34 hours, then we have 18 dollars per m. Two a one bike and $27 per m. Three a went bike, and this adds up 3 to $35 So now we have a natural system between your equations that can be solved by writing in the matrix form. This is would be to 3 34 18 27 three, 35. Now we just do some reductions. So we subtract row two or nine times we tracked nine times were a one from road route to, and that will get us to 3 34 00 29. So now, from the last row, we see that this system of when you're equations is impossible to solve. So this in question is impossible to answer. So all in all, it is not possible to use up Oh, our time and money any day.

Okay here we have a bicycle factory, it produces 100 bikes for a cost of $10,500. So let's write that as an ordered pair for 100 bikes, 10,500. Now we have another ordered pair this time it's $120 cost 1100. And we're going to be finding that daily fixed cost and also the marginal cost per bike. So the daily fixed costs, you might notice this as be in a linear equation where the marginal cost per bicycle, you might consider that that is your slope right? A cost per bicycle. It's kind of our changes are Y. Value over change in X value. So let's go ahead and find that slope first. That value of M. So we're going to take our 1 11,000 minus R 10,500 then we're going to divide that by the 1 20 minus 100. So that gives us 500 divided by 20 And that is 25. So that's going to be like $25 per each bicycle. So for one bicycle. So the answer is our first question. Our second question. To find that daily fixed costs, we can write our equation, Y equals mx plus B. Because B is the initial value as if no bikes right, X equals zero. Like no bikes have been found. So you have to use one of your points. I just decided to use that first point with 110,500 and placed it in for my X. and Y. And then I can solve for B. So b ends up being $8,000, so that is our daily fixed cost.

So for this question, we're asked him with the function for the cost of a bicycle. So first, well, you know, every single bike costs $125 for every bike made. Where's the Notah? Has fixed costs of $26,000. So this is our function to represent the bicycle factories costs.


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