Q$.1$ Set. $($A$)($a$)$ Residents of Mill River have fond memories of ice skating at a local park. An artist has captured the experience in a drawing and is hoping to reprodure it and self framed copies to current and former residents. He thinks that if the market is good, be can sell $400$ copies of the elegant version at $$125$ each. If the market is not good, he will sell only $300$ at $$90$ each. He can make a deluxe version of the same drawing instead. He feels that if the market is good, be can sell $500$ copies of the deluxe version at $$100$ each. If the market is not good, he will sell only $400$ copies at $$70$ each. In either case, production costs will be approximately $$35,000.$ He can also choose to do nothing. If he believes there is a $50\%$ probability of a good market, what should he do$?$ Why? $[8$ marks$]$

$($b$)$ Stapleton Manufacturing intends to increase capacity through the addition of new equipment. Two vendors have presented proposals. The fixed cost for proposal $A$ is $$65,000,$ and for proposal B$,$ $$34,000.$ The variable cost for $A$ is $$10,$ and for B$,$ $$14.$ The revenue generated by each unit is $$18.$ At an expected volume of $8,300$ units, which altemative should be chosen? $[2$ marks$]$