The Tech Student Government Association (SGA) has several campus projects it undertakes each year and its primary source of funding to support these projects is a T-shirt sale in the fall for what is known as the “orange effect” football game (with orange being one of Tech’s colors). The club’s publicized (media) objective is for everyone in the stadium to wear orange. The club’s financial goal is to make a profit of $150,000, but in order to have a significant number of fans buy the shirts and wear them to the game, it doesn’t want to price the T-shirts much more than $6. The stadium seats 62,000 fans, and the SGA would like to sell approximately 45,000 orange T-shirts to achieve the desired orange effect, which it’s relatively confident it can do. It will cost $100,000 to purchase, silk-screen print, and ship this many T-shirts. The SGA sells the shirts through three sources: online, the two Tech bookstores, and a local independent bookstore. While the bookstores don’t expect to share in the profits from the sale of the shirts, they do expect for their direct costs to be covered, including labor, space, and other costs. The two Tech bookstores charge the SGA $0.35 per shirt, and the local independent store charges $0.50 per shirt. The cost per sale online (including handling, packaging, and shipping) is $2.30 per shirt. The SGA estimates that it will sell 50% of the shirts at the two Tech bookstores, 35% at the local bookstore, and 15% online. If the SGA sells the T-shirts for $6 and if it sells all the shirts it orders, will it make enough profit to achieve its financial goal? If not, at what price would the SGA need to sell the T-shirts, or how many would the SGA have to sell to achieve its financial goal?
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