Question $2$

Jamie and Alex, a married couple, have been operating their food truck, Silver Spoon Delights, for a year. Specializing in gourmet sandwiches and salads, their motto is 'Fresh and Fast.$\text{'}$ Based in Fresno, California, they've seen consistent business and have started to build a loyal customer base. Besides their daily operations, they've participated in local festivals and taken catering jobs.

Recently, they received an invitation to join the 'Farm Fest' $$ a popular agricultural show in a neighboring town, Clovis, located $50$ miles from Fresno. The event promises $600$ attendees, and Silver Spoon Delights would be the exclusive food vendor. While the opportunity seems lucrative, Jamie and Alex recall a past event where promised numbers didn't materialize. They also consider the distance, potential costs, and the business they might miss in Fresno.

At special events, the couple modifies their menu to serve just the gourmet sandwiches, eliminating the salads. This speeds up service and allows them to offer sandwiches at $$8$ each. By doing so$,$ their packaging costs reduce, leading to a total variable cost of $$6$ per customer.

However, participating in 'Farm Fest' would bring additional costs. The organizers have suggested a $$80$ donation. The truck runs on diesel, and the round trip to Clovis would cost an additional $$80.$ Since the truck has limited seating, if Jamie drives the truck, Alex would need to drive their car, adding an estimated fuel cost of $$25.$ Staying in Fresno would avoid these costs.

Though the organizers assure them exclusivity, Jamie and Alex are wary. Past experiences have taught them that unexpected competitors can appear. They decide to prepare for multiple scenarios.

While Fresno has been profitable, 'Farm Fest' presents an opportunity to tap into a new market. Jamie and Alex realize that while numbers are crucial, the decision involves other factors. They sit down to evaluate their options.

Based on the given data, evaluate whether Silver Spoon Delights should participate in 'Farm Fest.$\text{'}$ Consider all costs, potential revenues, and risks. Prepare a report detailing your analysis and recommendations.

Questions:

$1.$ Calculate the total variable costs and total fixed costs for Silver Spoon Delights if they decide to participate in 'Farm Fest.

$2.$ Based on the organizers' estimate of $600$ attendees, how many sandwiches would Silver Spoon need to sell at 'Farm Fest' to break even? What would be the total revenue at this break$-$even point?

$3.$ If Silver Spoon Delights expects a $50\%$ turnout of the estimated attendees and each customer purchases one sandwich, calculate the total profit or loss for participating in 'Farm Fest.$\text{'}$

$4.$ If Silver Spoon Delights expects a $75\%$ turnout of the estimated attendees and each customer purchases one sandwich, Silver Spoon Delights also expects to compete with two other food vendors, calculate the total profit or loss for participating in 'Farm Fest.$\text{'}$

$5.$ Based on your calculations and other qualitative factors, should Silver Spoon Delights participate in 'Farm Fest'? Justify your answer.