$1)$ The construction of a new hockey arena is currently in the development planning stage. The National Hockey League is not certain of the number of luxury seating boxes planned for the upper section of the arena, as well as their profitability. Typically, large companies and high net$-$worth people may buy a seating box in the upper section of the arena for $$225,000.$ The fixed costs of construction for the upper section seating box area is expected to be $$3,750,000,$ with a variable cost of $$120,000$ for each box constructed.

a$.$ Calculate the breakeven point for the number of upper section seating boxes in proposed arena? What is the contribution margin per upper section seating box constructed?

b$.$ Planning stage schematics of the arena show that space is available for the construction of up to $30$ upper section seating boxes. The marketing department for the project indicates that there are interested buyers and that all $30$ could be sold if constructed. Do you recommend that these upper section seating boxes are constructed? What profit$/$loss is expected from building these boxes?

c$.$ How will the break$-$even point change if the fixed cost decreases by $20\%,$ variable cost increase by $10\%$ and selling price decreases by $8\%?$