Your company is considering two products for a new market. The probability distribution for the demand for the two products is presented in the table below. Q$($A$)$ and Q$($B$)$ are the possible quantities of each product that could be sold. P$($A$)$ and P$($B$)$ are the probabilities of selling the corresponding quantities.

Q$($A$)$ P$($A$)$ Q$($B$)$ P$($B$)$

$100000\mathrm{.}15100000\mathrm{.}25$

$300000\mathrm{.}20300000\mathrm{.}30$

$500000\mathrm{.}40500000\mathrm{.}35$

$600000\mathrm{.}25600000\mathrm{.}10$

You have the following additional information: The projected selling price for DESIGN $"$A$"$ is $$60.$ The fixed cost of its production is$$75,000.$ Its variable cost is $$35$ a unit. The selling price for DESIGN $"$B$"$ is $$80.$ Its fixed cost of production is $$110,000.$ The variable cost of production is $$48$ a unit. Which project is expected to be more profitable?