The Churrozilla Food Truck

The Churrozilla Food Truck produces specialty churros that are primarily sold at special events, such as football games and concerts. Ricky, the owner, is trying to decide how many to produce for an upcoming game. During the game, Ricky can sell Churros for $3 each (536 per dozen].

His competition is selling soft pretzels for $9 each, so Ricky thinks he’s giving the fans a bargain. However, when the game ends, any remaining ch urro dough is sold for $1 each {$12/dozen].

It costs Ricky $15 to buy and make a dozen churros. It sounds expensive, but includes the cost of the vehicle, the fees that the stadium charges for the right to sell, in addition to the cost of the ingredients and supplies to make the churros. Ricky’s estimate of demand for churros [in dozens} is the following:

Demand [in dozens) Probability 1800 dozen 0.05 2000 0.10 2200 0.15 2400 0.25 2600 0.30 2800 0.10 3000 0.05 a. What is the service rate (or optimal fractile}? b. How many churros [to the nearest hundred dozen) should Ricky produce for the upcoming game?