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Annie's Homemade Ice Cream is considering starting a Fan Club to grow its revenues, particularly during the winter months. Each member of the Fan Club would pay a monthly fee to obtain the following benefits:

One free t$-$shirt received at the time of enrollment. Each t$-$shirt costs Annie's $$9\mathrm{.}00.$

One free ice cream flight per month. Each flight consists of two$-$ounce servings of four flavors. Annie's cost per flight is $$1\mathrm{.}60.$

Eligibility to spin the prize wheel after each increment of $12$ servings purchased. Annie's estimates each member will buy four servings of ice cream per month; therefore, being eligible to spin the prize wheel once every three months, or four times a year. The average cost of each prize awarded when a fan club member spins the prize wheel is $$5\mathrm{.}00.$

In addition, Annie's uses $$1\mathrm{.}00$ per member per month to $$buy$$ ice cream for $$5\mathrm{.}00$ per serving. The company then donates the ice cream purchased by fan club members to community organizations such as Big Brothers$/$Big Sisters, public schools, and first responders. Annie's cost per pre$-$packaged, donated serving is $$1\mathrm{.}40.$

Annie's estimates customers who are not members of the fan club buy two servings of ice cream per month, whereas the fan club$$s benefits motivate loyal members to buy four servings per month. The price per serving and ingredient cost per serving are $$5\mathrm{.}00$ and $$1\mathrm{.}20,$ respectively.

The company is asking your recommendation whether it should charge members $$12$ per month $($or $$144$ for an annual membership$)$ or $$10$ per month $($or $$120$ for an annual membership$).$