Question

Dalco manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formlua P = -3x^2 + 6x + 10, where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. FInd the mximum weekly profit.

Answer 1

Given a function:

`y=ax^2+bx+c`

The vertex is the point V(h,k) given by:

`\begin{gathered} h=(-b)/(2a) \\ k=y(h) \end{gathered}`

Therefore:

`\begin{gathered} y=-3x^2+6x+10 \\ a=-3 \\ b=6 \\ c=10 \end{gathered}`
`h=(-6)/(2(-3))=(-6)/(-6)=1`
`k=y(h)=-3(1)^2+6(1)+10=-3+6+10=13`

The company needs to produce 1000 per week in order to earn its maximum profit of $1300 dollars