The charity will maximize its profit when it reaches the vertex of the quadratic equation.
The x-coordinate of the vertex is given by:
𝑥 = −𝑏/2𝑎
where 𝑏 = 1250 and 𝑎 = −35.
Substituting these values and simplifying:
𝑥 = −1250/(2(−35))
𝑥 = 17.86
Therefore, the charity will maximize its profit when they sell T-shirts for $17.86 each.
The amount of money that a local charity earns by selling T-shirts at a mall depends on the price of each T-shirt. The monthly profit, 𝑦, in dollars is given by the quadratic equation 𝑦 = −35𝑥2 + 1250𝑥 − 6500 where 𝑥 represents the price of each T-shirt Under what circumstances will the charity maximize its profit (make the most money)?
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