Humber Bakery needs to decide how many units of its new Rexdough (nicknamedRex) bread to bake at the beginning of each day. Because the bakery prides itself as the maker of the freshest premium bread in town, units that are unsold by the end of the day are discarded and considered loss. Each Rexdough bread costs$1.47to produce and sells for$4.37. Humber's objective is to maximize daily gross profit. The bakery's daily production system is set up as follows:

Production SystemLight Production (26,000 loaves)Moderate Production (32,000 loaves)Heavy Production (48,000 loaves)

Humber Bakery is uncertain about the demand forRexbut believes that one of the following states of nature (outcomes) will occur:

States of NatureLow Demand (20,000 loaves)Medium Demand (30,000 loaves)High Demand (40,000 loaves)

Note: The bakery cannot sell more than it produces. For example, if production level is moderate (32,000) and demand is low (20,000), the bakery will sell only 20,000 units but will incur the costs of producing 32,000 units. The corresponding gross profit will be $4.37(20,000) - $1.47(32,000) = $40,360.

PART A

1. Calculate the payoff (daily gross profit, in dollars) for each production/demand level combination and complete the following payoff table.

Low Demand

Medium DemandHigh DemandLight

ProductionModerate

ProductionHeavy

Production

After some deliberations, the bakery's manager arrived at the following probabilities of the states of nature (outcomes):Probabilities for States of NatureP

(

Low Demand

)

=

P(Low Demand)=

0.5P

(

Medium Demand

)

=

P(Medium Demand)=

0.3P

(

High Demand

)

=

P(High Demand)=

0.2

a) What is the expected monetary value of the optimal decision.

EMV = $

b) The optimal decision isSelect an answer

Light

Moderate

Heavy

production.