Preliminary plans are underway for construction of a new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may purchase a box for $$300,000.$ The fixed construction cost for the upper$-$deck area is estimated to be $$4,500,000,$ with a variable cost of $$150,000$ for each box constructed.

a$.$ What is the breakeven point for the number of luxury boxes in the new stadium?

b$.$ Preliminary drawings for the stadium show that space is available for the construction of up to $50$ luxury boxes. Promoters indicate that buyers are available and that all $50$ could be sold if constructed.

i$.$ What is your recommendation concerning the construction of luxury boxes?

ii$.$ What profit is anticipated?

The use of graphical method is recommended.