Summary: We introduce the isotonic regression knapsack problem \[ \min(1/2)\sum^ n_{i=1} \{d_ i x^ 2_ i- 2\alpha_ i x_ i\},\text{ s.t. } \sum^ n_{i=1} a_ i x_ i= c,\;x_ 1\leq x_ 2\leq\cdots\leq x_{n- 1}\leq x_ n, \] where each \(d_ i\) is positive and each \(\alpha_ i\), \(a_ i\), \(i=1,\dots,n\), and \(c\) are arbitrary scalars. This problem is the natural extension of the isotonic regression problem which permits a strong polynomial solution algorithm. An approach is developed from the Karush-Kuhn-Tucker conditions. By considering the Lagrange function without the inequalities, we establish a way to find the proper Lagrange multiplier associated with the equation using a parametric program, which yields optimality. We show that such a procedure can be performed in strong polynomial time, and an example is demonstrated.