Q=sqrt((2KD)/(F)) For companies that monitor the inventory of a product, the equation gives Q, the quantity to order of the product as a function of K, the ordering cost, D, the annual demand for the product and F, the average holding cost of the product. Which of the following equations correctly gives the annual demand for the product in terms of the quantity to order, the ordering cost, the annual demand, and the average holding cost for the product? Choose 1 answer: (A) D=sqrt((2FQ)/(K)) (B) D=sqrt((FQ)/(2K)) (C) D=(2FQ^(2))/(K) (D) D=(FQ^(2))/(2K)

Question

Q=sqrt((2KD)/(F)) For companies that monitor the inventory of a product, the equation gives  Q, the quantity to order of the product as a function of  K, the ordering cost,  D, the annual demand for the product and  F, the average holding cost of the product. Which of the following equations correctly gives the annual demand for the product in terms of the quantity to order, the ordering cost, the annual demand, and the average holding cost for the product? Choose 1 answer: (A)  D=sqrt((2FQ)/(K)) (B)  D=sqrt((FQ)/(2K)) (C)  D=(2FQ^(2))/(K) (D) D=(FQ^(2))/(2K)

Bytelearn · Accepted Answer

Start with given equation: We start with the given equation for Q: $$ Q = \sqrt{\frac{2KD}{F}} $$ To find D in terms of Q, K, and F, we need to solve this equation for D.Square both sides: First, we square both sides of the equation to eliminate the square root: $$ Q^2 = \frac{2KD}{F} $$Multiply by F: Next, we multiply both sides of the equation by F to get rid of the fraction: $$ FQ^2 = 2KD $$Divide by 2K: Now, we divide both sides of the equation by 2K to solve for D: $$ D = \frac{FQ^2}{2K} $$Check given options: We check the options given to see which one matches our derived expression for D: (A) $ D = \sqrt{\frac{2FQ}{K}} $ - This is not correct. (B) $ D = \sqrt{\frac{FQ}{2K}} $ - This is not correct. (C) $ D = \frac{2FQ^2}{K} $ - This is incorrect because it has an extra factor of 2. The correct expression is $ D = \frac{FQ^2}{2K} $, but this is not one of the options provided.Since none of the given options match our derived expression for D, there seems to be an error in the options provided.

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