To earn some money, John is thinking of starting up a "Back$-$Yard $BB{Q}^2$ stand

at his university campus this summer. The basic $"$BBQ$"$ equipment will cost

$$2690,$ and the variable cost $($VC$)$ for each $"$BBQ Meal" is estimated to be $$6\mathrm{.}75.$

He thinks he will be able to sell each $"$BBQ Meal" for $$10\mathrm{.}00.[20$ points$]$

a$.$ What is the break$-$even quantity of $"$BBQ Meals" for John's "Back$-$Yard

$BB{Q}^n$ stand? $[10$ points$]$

b$.$ If John's goal for profit is $$2500$ for his fall semester tuition, how many

$"$BBQ Meals" would he need to sell in the summer to reach his goal? $[10$

points$]$

Peter is thinking of starting up a "Personal Financial Services" consultation in his

spare time. The basic office equipment will cost $$2285,$ and the variable cost $($VC$)$

for each consultation is estimated to be $$14\mathrm{.}60.$ He plans to bill each client $$65$

per consultation? $[30$ points$]$

a$.$ What is the break$-$even quantity of consultations for Peter's "Personal

Financial Services" operation? $[10$ points$]$

b$.$ If Peter's profit goal is $$1000,$ how many consultations would he need to

reach his goal? $[10$ points$]$

c$.$ Briefly explain the concept of a "Contribution Margin" and demonstrate how

the Contribution Margin $($CM$)$ determined from the information above can

be used to determine the same break$-$even quantity determined in part $($a$)?$

$[10$ points$]$