Problem $5$S$-14($Algo$)$

The director of social services of a county has learned that the state has mandated additional information requirements. This will place an additional burden on the agency. The director has identified three acceptable alternatives to handle the increased workload. One alternative is to reassign present staff members, the second is to hire and train two new workers, and the third is to redesign current practice so that workers can readily collect the information with little additional effort. An unknown factor is the caseload for the coming year when the new data will be collected on a trial basis. The estimated costs for various options and caseloads are shown in the following table:

CASELOAD

Moderate High Very High

Reassign staff $ $45*5550$

New staff $505050$

Redesign collection $758580$

$*$Cost in $ thousands.

After contemplating the caseload question, the director of social services has decided that reasonable caseload probabilities are $0\mathrm{.}20$ for moderate, $0\mathrm{.}40$ for high, and $0\mathrm{.}40$ for very high.

a$.$ Which alternative will yield the minimum expected cost?