A DECISION PAYOFF MODEL

Albion store is contemplating the quantity of the latest smartphones $(150,200,$ or $250$ units$)$ to order and potentially sell during the upcoming tech expo. The store purchases each smartphone at $$350$ and sells them for $$500$ each. Any unsold smartphones after the expo will be liquidated at a reduced price of $$250$ each during a clearance event. To calculate their overall profit, they have formulated the following profit $($payoff$)$ model:

Profit $=($retail price $\backslash$times min$\{$order quantity, customer demand$\})-($purchase cost $\backslash$times order quantity$)+$ revenue from the clearance event $($if any$)$

Clearance event revenue $=$ max $[$ clearance price $\backslash$times $($order $-$ demand$),0]$

For example, if they order $250$ units and demand is $200$ units, their gross profit will be

$($$$500\backslash$times $200)-($$$350\backslash$times $250)+$ $$250\backslash$times $(250-200)=$ $$25,000$

Note: Clearance revenue can be only realized if supply is greater than demand and there is no penalty for excess demand.

Use the given information to complete the following payoff table.

$$ PAYOFF TABLE

Demand $=$

$150$ units Demand $=$

$200$ units Demand $=$

$250$ units

Order $=$

$150$ units

Order $=$

$200$ units

Order $=$

$250$ units