A firm must decide whether to construct a small, medium, or large manufacturing plant for pre-fabricated wall panels. A consultant's report indicates a 20% probability that demand will be low and an 80% probability that demand will be high.

If the firm builds a small facility and demand turns out to be low, the profit will be 42m. If the demand turns out to be high, the firm can either subcontract and realize the profit of 42m or expand for a profit of 48m.

The firm could build a medium-size facility as a hedge: If demand is low, its profit is estimated at 22m; if demand turns out to be high, the firm could do nothing and realize a profit of 46m, or it could expand and realize a profit of 50m.

If the firm builds a large facility and demand is low, the loss will be 20m, whereas high demand will result in a profit of 72m. What should the company do?