School of Troy decided to award prizes to the most punctual and the most obedient student. The sum of two prizes is $\$150$ and this product is $\$5600.$ Which of the following can be the equation to represent the above condition ?

Question

$\begin{array}{1 1} (a)\; x^2+150x+5600 = 0 \\ (b)\; x^2-150x-5600=0 \\ (c)\; x^2-150x+5600 = 0 \\ (d)\; x^2+150x-5600 =0 \end{array}$