Question

Someone please help me with this equation step by step

Answer 1

Case: Quadratic

Method:

a) She makes a profit between the prices where the Profit P(x) is greater than 0.

Plotting a graph

From the graph,

She makes a profit when the prices are between $0.25 and $49.75

b)

To make the maximum profit

`\begin{gathered} P(x)=-2x^2+100x-25 \\ P(x)=-2[x^2-50x]-25 \\ P(x)=-2[x^2-50x+625-625]-25 \\ P(x)=-2[(x-25)^2-625]-25 \\ P(x)=-2(x-25)^2+1250-25 \\ P(x)=-2(x-25)^2+1225 \\ When\text{ }the\text{ }price\text{ }x=25\text{ }the\text{ }profit\text{ }is\text{ }maximum \\ P(25)=1225 \end{gathered}`

Final answers:

a) Between $0.25 and $49.75

b) Price, x = 25