Question

Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p=-0.5x^(2)+25x-173 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $102 ?

Answer 1

`\Large \textsf{Read below}`

Explanation:

`\Large \text{$ \sf p = -0.5x^2 + 25x - 173$}`

`\Large \text{$ \sf 102 = -0.5x^2 + 25x - 173$}`

`\Large \text{$ \sf -0.5x^2 + 25x - 173 - 102 = 0$}`

`\Large \text{$ \sf -0.5x^2 + 25x - 275 = 0$}`

`\Large \text{$ \sf 0.5x^2 - 25x + 275 = 0$}`

`\Large \boxed{\text{$ \sf a = 0.5,\: b = -25,\:c = 275$}}`

`\Large \text{$ \sf \Delta = b^2 - 4.a.c$}`

`\Large \text{$ \sf \Delta = (-25)^2 - 4.(0.5).(275)$}`

`\Large \text{$ \sf \Delta = 625 - 550$}`

`\Large \text{$ \sf \Delta = 75$}`

`\Large \text{$\sf x = (-b \pm √(\Delta))/(2a) = (25 \pm √(75))/(1) \rightarrow \begin{cases}\sf{x' = 25 - √(75)}\\\\\sf{x'' = 25 + √(75)}\end{cases}$}`

`\Large \boxed{\boxed{\textsf{x = \$16,34}}}`