Part $3$: Customer Profitability Analysis $(20$ marks$)$

Mark$$s Comedy Emporium provides entertainment for birthday parties. Over the last year Mark$$s has entertained at over $150$ birthday parties and it seems the Mark$$s business is booming! Customers generally must book six to eight months in advance to secure a spot, and the company has parties booked solid for the next six months. Business is busy, customers are extremely happy, and employees are happy, but Mark is barely breaking even. He cannot understand, with his business being so successful, why he is barely able to pay himself a wage. Mark has asked you to help him figure out what he is doing wrong.

The services provided at each party vary. Some customers only want a clown to perform, and they handle the other party details themselves. Other customers want a full package$$clown$,$ food, cake, entertainment, cleanup, party favours, decorations, and costumes for the kids. Mark$$s can provide the following services at a party:

$$ Clown: Most parties include a clown who performs for one hour at the party. Mark pays a clown $$40$ per party.

$$ Food $($excluding cake$)$: When customers order food for their party through Mark$$s$,$ he outsources this service to Carl$$s Catering. Carl charges an average of $$12$ per child for food.

$$ Cake: Mark sources birthday cakes through his sister, Sarah, who runs a small bakery and makes custom cakes for Mark$$s$.$ Her smallest cake is $8$ in diameter $($serves up to $10$ kids$)$ and costs $$40.$ She also makes a $10$ cake for $$60($serves up to $20$ kids$).$

$$ Cleanup: Mark$$s provides cleanup service. Cleaning staff are paid $$15$ per hour, and cleanup averages two hours per $20$ kids. Cleanup is a variable cost based on number of kids attending the party.

$$ Party favours: Party favour bags can also be ordered through Mark$$s$.$ These cost $$5$ per bag to assemble.

$$ Decorations: Mark$$s will also fully decorate a party. Decorating staff are paid $$15$ per hour, and it takes one hour to decorate a party for $20$ kids. Decorations cost an average of $$50$ for party of $20$ kids. Decorating staff and decorations are fully variable based on the number of kids.

$$ Costumes. Mark$$s also provides costumes for parties so that kids can dress up based on a theme. On average, costumes cost $$40$ each and can be worn $25$ times before they need to be replaced. Costumes are cleaned after each use at a cost of $$5$ each.

Mark has set up a fee schedule for each service as follows:

Service Fee charged to customer

Clown $$60$ per party

Food $$15$ per child

Cake $$2$ per child

Cleanup $$2$ per child

Party favours $$6$ per child

Decorations $$2$ per child

Costumes $$6$ per child

In a two$-$week period, Mark catered six parties with the following services:

Customer $123456$

# of kids attended $20254515512$

Clown Y Y Y Y N Y

Food services Y Y N N Y N

Cake Y N N Y Y N

Cleanup Y Y N N Y N

Party favours Y Y N N Y N

Decorations Y Y Y N Y N

Costumes N N Y N Y N