Kresge Lodging has an elite program for its card members. There are three levels, based on total nights stayed: Diamond $(50$ nights or more$)$; Platinum $(25$ nights or more$)$; and Base $($fewer than $25$ nights$).$ In order to facilitate reservations and answer customer questions, Kresge Lodging provides access to special customer service representatives, who work exclusively with the designated level $($Diamond$,$ and so on$).$ Customer representatives receive salaries plus bonuses of $5$ percent of customer gross margin. The company provides various perquisites $($free nights, upgrades, and so on$)$ to its members, with $75$ percent of the cost of the perquisites used for the benefit of Diamond members, $20$ percent for Platinum members, and $5$ percent for Base members.

Customer CostsTotalDiamondPlatinumBaseNumber of members$160,00021,00055,00084,000$Average customer representative salary$$$ $80,000$$ $53,000$$ $42,000$Number of representatives$281585$Perquisite costs$ $6,900,000$Average annual gross margin per customer$$$ $1,200$$ $400$$ $200$

The gross margin received by Kresge is the amount received from the participating hotels for a customer's stay.

Required:

What is the excess of gross margin over customer costs for each category of customer?

Customer CostsTotalDiamondPlatinumBaseNumber of members$160,00021,00055,00084,000$Average customer representative salary$$$ $80,000$$ $53,000$$ $42,000$Number of representatives$281585$Perquisite costs$ $6,900,000$Average annual gross margin per customer$$$ $1,200$$ $400$$ $200$

The gross margin received by Kresge is the amount received from the participating hotels for a customer's stay.

Required:

What is the excess of gross margin over customer costs for each category of customer?

Which customers are more profitable?