1. [10pts) A fence is to be built to enclose a rectangular area of 210 square feet. The fence along three sides is to be made of material that costs 6 $ per foot, and the material for the fourth side costs 16 $ per foot. a) Find the length L and width W (with W 5 L) of the enclosure that is most economical to construct. b) Find the minimum cost c) complete the sentence that answer the question Solution steps: (2pts) Sketch a picture (2pts) Build a math model: Objective function 0F. and constrains (2pts) Find the optimal values for the OP. (3pts) Justify your answer using 1*"t derivative test (lpts) Answer the question using exact and approximate values (see a) , b), c ) ) P'PP'P!' Answer: exact and approximate up to 2 decimals a) L = W = b) minimum cost C = c) Complete the sentence: The dimensions of the fence that is most economicoi to construct are x and the cost of this fence is 2. Use properties of logarithms to write as a single logarithm: 1 3ln x - 7lny+5 In z = N