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?

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?

Bytelearn · Accepted Answer

Square Both Sides: We have the original equation for the quantity to order: $$ Q = \sqrt{\frac{2KD}{F}} $$ We need to solve for D, the annual demand for the product. To do this, we will square both sides of the equation to eliminate the square root. $$ Q^2 = \frac{2KD}{F} $$Multiply by F: Next, we will multiply both sides of the equation by F to get rid of the fraction. $$ Q^2 \times F = 2KD $$Divide by 2K: Now, we will divide both sides of the equation by 2K to solve for D. $$ \frac{Q^2 \times F}{2K} = D $$Isolate Annual Demand: We have successfully isolated D, the annual demand for the product, in terms of Q, K, and F. $$ D = \frac{Q^2 \times F}{2K} $$ This is the equation that gives the annual demand for the product in terms of the quantity to order, the ordering cost, and the average holding cost.

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