The town council of Frostbite, Ontario, is trying to decide whether to build an outdoor skating rink which would cost $1 million and last for only one season. Operating costs would be zero. Yearly passes would be sold to anyone who wanted to use the rink. If p is the price of the pass in dollars, the number demanded would be q = 1200 - .6p. The council has asked you to advise them on building the rink. You should tell them that

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To break even, the rink must generate $1 million in revenue. The revenue generated by ticket sales is given by q*p, where q = 1200 - 0.6p. Therefore, the revenue function can be expressed as R(p) = p(1200 - 0.6p). To find the price that maximizes profit, we must first find the quantity that maximizes revenue. This occurs when p = 1000, which means that q = 600. The maximum revenue is then R(1000) = 600,000. This is below the construction cost of $1 million, so revenues won't cover costs at any ticket price. Additionally, since there are no operating costs, profits are simply equal to revenue. Since revenues don't cover costs, there is no profit to be made, meaning that total consumer surplus from the rink will be negative. Therefore, the best choice is D.

The Town Council of Frostbite, Ontario, Is Trying to Decide