Question

If x represents the number of admissions counselors, how many admissionscounselors should the college employ to maximize its profit?

Answer 1

Given,

The function for the profit is,

`y=-10x^2+1500x-35000`

Differentiating the function with respect to x then,

`\begin{gathered} (dy)/(dx)=(d)/(dx)(-10x^2+1500x-35000) \\ =-20x+1500 \end{gathered}`

Check for maximum by second order differentiation,

Differentiating the function with respect to x then,

`\begin{gathered} (d^2y)/(dx^2)=(d)/(dx)(-20x^{}+1500) \\ =-20 \end{gathered}`

Negative sign shows the maximum.

For maximum, taking dy/dx=0 then,

`\begin{gathered} -20x+1500=0 \\ 1500=20x \\ x=75 \end{gathered}`

Subsituing the value of x in the function then,

`\begin{gathered} y=-10(75)^2+1500*75-35000 \\ =-56250+112500-35000 \\ =21250 \end{gathered}`

Hence, 75 admissions counselors should the college employ to maximize its profit.