A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being

0.40,

0.35,

and

0.25,

respectively.A small facility is expected to earn an after-tax net present value of just

$12,000

if demand is low. If demand is average, the small facility is expected to earn

$15,000;

it can be increased to medium size to earn a net present value of

$30,000.

If demand is high, the small facility is expected to earn

$25,000

and can be expanded to medium size to earn

$50,000

or to large size to earn

$75,000.

A medium-sized facility is expected to lose an estimated

$25,000

if demand is low and earn

$90,000

if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of

$125,000;

it can be expanded to a large size for a net payoff of

$165,000.

If a large facility is built and demand is high, earnings are expected to be

$180,000.

If demand is average for the large facility, the present value is expected to be

$80,000;

if demand is low, the facility is expected to lose

$50,000.

What should management do to achieve the highest expected payoff?

The management should build a

Large,medium, or small facility please choose

in order to achieve the highest expected payoff of

$__________

(Enter your response as a whole number.)