*I just need help with the last paragraph, I have the answers to the first 2. Yo
ID: 3192798 • Letter: #
Question
*I just need help with the last paragraph, I have the answers to the first 2. You are a landscape designer. A client has asked you to design a plan to enclose a rectangular garden having 10,000 m^2 of area. the north and south sides are to be bounded by wooden fence , which costs $20/m; the east and west sides are to be bounded by rhododendrons, which cost $50/m. find the dimensions of the garden that minimize the total cost of the fencing and shrubbery. A 10,000 m^2 garden is to be enclosed on the north and south by material A, which costs a dollars per meter, and on the east and west by material B, which cost b dollars per meter. Find the dimensions of the garden that minimize the cost of enclosing the garden. The dimensions should be in terms of a and b. * This is what I need help with. What does the template tell you about the dimensions of the garden when a=b? When a = 4b? When a = (1/4)b? Does it agree with the dimensions you found for the rhododendron/wooden fence-enclosed garden? What happens if the are of the garden is to be something other than 10,000 m^2?Explanation / Answer
just assume that the dimension of the garden is aXb take the sides with length as 'a' as north-south side and the side with 'b' m dimension as the east-west side, then as the area of the garden is 10,000 m^2 therefore first equation that you get is a*b=10000, now you need to fence the north south side, so the total cost of fencing would turn out to be, 2*a*20=40*a $ and similarly the total cost of bounding by rhododendron would cost 2*b*50=100*b $ therefore the total cost that one has to incur would be T= 40a+100b, now substitute b=10000/a, therefore T(a)=40a+1000000/a , then differentiate wrt a and you get 40-1000000/(a^2) equate it to 0 and you will get a, similarly you will get b, initially when you take a and b as the dimension , it takes into consideration all the possibilities, the possibilities might be that a=b or anything else, you get one equation that tells you b in terms of a (i.e; you get one dimension in terms of another dimension) so the total cost will only depend on one of the dimensions, all you have to do is differentiate and equate the T'(a)=0 to get that value of 'a' which minimizes the total cost, proceeding further you will also get 'b' as it is a function of 'a' this is how you need to solve any problem of this kind, feel free to ask any more doubt or query regarding this.. :) please rate asap.
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