With the rapid growth of threats, sophistication and diversity in the manner of intrusion, traditional belt barrier systems are now faced with a major challenge of providing high and concrete coverage quality to expand the guarding service market. Recent efforts aim at constructing a belt barrier by deploying bistatic radar(s) on a specific line regardless of the limitation on deployment locations, to keep the width of the barrier from going below a specific threshold and the total bistatic radar placement cost is minimized, referred to as the Minimum Cost Linear Placement (MCLP) problem. The existing solutions are heuristic, and their validity is tightly bound by the barrier width parameter that these solutions only work for a fixed barrier width value. In this work, we propose an optimal solution, referred to as the Opt_MCLP, for the "open MCLP problem" that works for full range of the barrier width. Through rigorous theoretical analysis and experimentation, we demonstrate that the proposed algorithms perform well in terms of placement cost reduction and barrier coverage guarantee.