Calgary has decided to build a new stadium for use by its professional hockey team, the Flames, as well as for concerts and other events requiring a large venue. To solicit creative design concepts, city council has decided to have a competition. The firm submitting a design that best fulfills the criteria developed by the city planning committee will earn revenues of $$1,000,000$ before consideration of design costs.Management at Big Sky Design is considering submitting a proposal. They know that a carefully developed design proposal will greatly increase the likelihood of winning, but such a design will be expensive to develop. Conversely, they could submit a less creative design that will be considerably cheaper to develop, but less likely to win. Big Sky Design is considering two proposals. The proposal cost and probability of success for each are as follows: Cost of Probability of Design Proposal Winning Proposal A $...................$ $$300,0000\mathrm{.}60$ Proposal B $...................$ $$100,0000\mathrm{.}20$ Design costs are assumed to be incurred at the beginning of the current year. Income taxes are $30\%.$ If Big Sky Design does not win the competition, the costs of the design proposal can be deducted from the revenues generated by other projects, which will reduce taxes payable. Required: $1.$ Which proposal would you recommend Big Sky Design submit to the design competition? Show all