Question 7 . Biscuit Co. has determined that their total monthly costs \( \$ C \) depend on how many biscuits \( b \) they bake by the quadratic \( C=(b-500)^{2}+150 \). Using this quadratic, by baking the optimal number of biscuits, their minimum monthly costs should be

To minimize the costs given by the quadratic equation \( C=(b-500)^{2}+150 \), observe that the term \( (b-500)^{2} \) reaches its minimum value of 0 when \( b=500 \). Substituting \( b=500 \) back into the equation gives \( C=0+150=150 \). Thus, by baking 500 biscuits, Biscuit Co. achieves their minimum monthly costs of \$150. This formula demonstrates the classic U-shaped curve of quadratic functions, where the vertex represents the minimum point. The concept applies in various businesses, from muffins to macaroons. So whether you’re scaling your cookie production or optimizing other production lines, always look for that sweet spot where costs dip!