McCleary Electronics Inc. seeks to $($a$)$ move forward immediately with a new TV design or $($b$)$ wait and ask their value analysis consultant for an evaluation of the added value of such new TV design. Under the first option, McCleary expects to sell $100,000$ units for $$550$ each with a likelihood of $0\mathrm{.}60$ if they will be successful in sales, or only $75,000$ units for also $$550$ per unit if the market has a $0\mathrm{.}40$ likelihood of not being in their favor. Under the value analysis option McCleary expects to sell $75,000$ at $$750$ per unit with a probability of $0\mathrm{.}7$ or sell $70,000$ units at $$750$ per unit with a probability of $0\mathrm{.}3.$ The value analysis consultant option $($b$)$ will cost McCleary an extra $$100,000.$ If they choose option $($a$)$ then the product design expected pay$-$off will be $ $\_\_\_\_\_.$Hint: draw a decision tree.