Assume that a system consists of five series elements. The initial reliability of all the elements is 0.9, each costing $1,000. All components must be improved so that they have a lower failure rate...

Assume that a system consists of five series elements. The initial reliability of all the elements is 0.9, each costing $1,000. All components must be improved so that they have a lower failure rate for the system to meet its goal of R_s
=0.9. Suppose that for three of the elements, each 50% reduction in failure probability adds $200 to the element cost; for the other two components, each 50% reduction in failure probability adds $300 to the element cost. Find the lowest cost system that meets the system goal of R_s
=0.9.