Question

for a certain company, the cost for producing x items is 45x+300 and the revenue for selling x items is 85x-0.5x^2. find two values of x that will create a profit of $50 part c: is it possible for the company to make a profit of $2,500?

Answer 1

the profit of the company is

`p(x)=-0.5x^2+85x-45x-300=-0.5x^2+40x-300`

for part B we get

`\begin{gathered} -0.5x^2+40x-300=50\rightarrow \\ 0.5x^2-40x+350=0 \\ x^2-80x+700=0 \\ (x-10)(x-70)=0 \\ x=10,x=70 \end{gathered}`

so, to make a profit of $50 the compay have to sell 10 or 70 units

for part c we get

`\begin{gathered} -0.5x^2+40x-300=2500\rightarrow \\ 0.5x^2-40x+2800=0 \\ x^2-80x+5600=0\text{ } \\ \text{ using the general formula we get that} \\ 80^2-4\cdot1\cdot5600<0\text{ so it is impossible to make a profit of 2500} \end{gathered}`