I have decided to pursue my lifelong dream and become a falafel vendor on the Campus Mall in Madison, Wisconsin. The business requires

I have decided to pursue my lifelong dream and become a falafel vendor on the Campus Mall in Madison, Wisconsin.  The business requires a $2,000 investment to become a Certified Falafel Vendor.  Furthermore, I must decide whether or not to invest in the economy cart or the deluxe cart.  The economy cart costs $3,000 while the deluxe cart costs $5,000.  However, the falafel maker on the deluxe cart requires less electricity.  As a result, the deluxe cart has a lower variable cost.  The cost per falafel is $3.50 and $5.00 for the deluxe and economy carts, respectively.  I plan to sell each falafel for $7.75.

a)      At what sales volume am I indifferent between buying the deluxe cart and the economy cart?  What is the profit at that sales volume?

b)      A third alternative is now available.  I can purchase falafels from a subcontractor for $5.75 per falafel and, therefore, do not need a cart (I still need to be certified).  For what range of production would each option be preferred?

 Suppose I do some more analysis to get a better understanding of the falafel market.  I determine that four sales volumes are possible: 500 units; 1,000 units; 2,000 units, 3,000 units and 4,000 units.  The probabilities of the sales volume occurring are:

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