2025 BVSS PRELIMS P1 Q13

The cost in thousands of dollars, \(C\), of producing \(n\) hundred pairs of a certain type of running shoes is given by the formula \(C=1.2n^2-14.4n+53.7\).

1. Find the initial cost of production.[1]
2. Express \(C\) in the form \(a(n+h)^2+k\) where \(a\), \(h\) and \(k\) are constants to be determined.[3]
3. Explain the meaning of the values of \(h\) and \(k\) in the formula as expressed in part (b).[1]
4. Find the maximum number of pairs of running shoes for which the cost will be 50 thousand dollars.[3]