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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)

Q=2KDF Q=\sqrt{\frac{2 K D}{F}} \newlineFor companies that monitor the inventory of a product, the equation gives Q Q , the quantity to order of the product as a function of K K , the ordering cost, D D , the annual demand for the product and F 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?\newlineChoose 11 answer:\newline(A) D=2FQK D=\sqrt{\frac{2 F Q}{K}} \newline(B) D=FQ2K D=\sqrt{\frac{F Q}{2 K}} \newline(C) D=2FQ2K D=\frac{2 F Q^{2}}{K}

Full solution

Q. Q=2KDF Q=\sqrt{\frac{2 K D}{F}} \newlineFor companies that monitor the inventory of a product, the equation gives Q Q , the quantity to order of the product as a function of K K , the ordering cost, D D , the annual demand for the product and F 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?\newlineChoose 11 answer:\newline(A) D=2FQK D=\sqrt{\frac{2 F Q}{K}} \newline(B) D=FQ2K D=\sqrt{\frac{F Q}{2 K}} \newline(C) D=2FQ2K D=\frac{2 F Q^{2}}{K}
  1. Given equation for Q: We start with the given equation for Q:\newlineQ=2KDFQ = \sqrt{\frac{2KD}{F}}\newlineWe want to solve for DD, so we need to isolate DD on one side of the equation.
  2. Squaring both sides: First, we square both sides of the equation to eliminate the square root:\newline(Q)2=((2KD)/F)2(Q)^2 = (\sqrt{(2KD)/F})^2\newlineThis simplifies to:\newlineQ2=(2KD)/FQ^2 = (2KD)/F
  3. Multiplying by F: Next, we multiply both sides of the equation by F to get rid of the division by F: F×Q2=2KDF \times Q^2 = 2KD
  4. Dividing by 22K: Now, we divide both sides of the equation by 22K to isolate D:\newline(FQ22K)=D(\frac{F \cdot Q^2}{2K}) = D
  5. Expression for D: Simplify the equation to find the expression for D:\newlineD=FQ22KD = \frac{F \cdot Q^2}{2K}\newlineThis matches option (C) from the given choices.

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